Type the equation of the line in the graph below. y=mx+b

1

Type in a point (x,y) that lies on this line.

1

Does(1,3) lie on this line?

yes

no

1

Instrukcije

Kliknite na karticu Grafikon (Grafikon 1, Grafikon 2 i tako dalje) za svaki grafikon koji trebate nacrtati.
Kliknite na pozadinu grafikona da biste dodali tačku. Dodajte dvije tačke da biste kreirali grafikon. Prevucite tačku ili unesite x i y koordinate da biste uredili njen položaj. Kliknite na tačku da biste je izbrisali.
Nakon što kreirate grafikon, možete označiti kućicu s isprekidanom linijom.

Recall that a solution to an equation is a (x,y) point that lies on the line of the equation and therefore makes the equation true.

For Example:

null

1

Is (1,3) a solution to the equation y=x+2?

yes

no

1

Type y<x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

4

Select EVERYTHING that's true about the graph of the inequality (#6) y<x+2.

The slope of the line for y<x+2 is negative.

The points on the line ARE NOT solutions.

The graph for y<x+2 is shaded below the line.

The points on the line ARE solutions (they make the inequality true).

The line for y<x+2 is dotted instead of solid.

The graph for y<x+2 is shaded above the line.

The points in the shaded region ARE solutions (they make the inequality true).

1

Is (1,3) a solution to the inequality? y<x+2?

yes

no

Notice in the example below, when = changes to < the point on the line is no longer a solution.

null

1

Type y\le x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

4

Select EVERYTHING that's true about the graph of the inequality (#9) y\le x+2.

The graph for y\le x+2 is also shaded below the line.

The line for y\le x+2 is dotted instead of solid.

The graph for y\le x+2 is shaded above the line.

The points on the line ARE NOT solutions.

The points on the line ARE solutions (they make the inequality true).

The slope of the line for y\le x+2 is negative.

The points in the shaded region ARE solutions.

The line for y\le x+2 is solid instead of dotted.

1

Is (1,3) a solution to the inequality? y\le x+2?

yes

no

Notice in the example below, when = changes to \leq the point on the line is still a solution!

null

1

Type y> x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

4

Select EVERYTHING that's true about the graph of the inequality (#12) y>x+2.

The line for y> x+2 is solid instead of dotted.

The line for y> x+2 is also dotted.

The graph for y> x+2 is shaded below the line.

The slope of the line for y> x+2 is negative.

The graph for y> x+2 is shaded above the line.

The points in the shaded region ARE solutions.

The points on the line ARE solutions (they make the inequality true).

The points on the line ARE NOT solutions.

1

Is (1,3) a solution to the inequality? y> x+2?

yes

no

1

Type y\geq x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

4

Select EVERYTHING that's true about the graph of the inequality (#15) y\geq x+2.

The points on the line ARE NOT solutions.

The graph for y\geq x+2 is shaded below the line.

The line for y\geq x+2 is solid instead of dotted.

The points in the shaded region ARE solutions.

The points on the line ARE solutions (they make the inequality true).

The slope of the line for y\geq x+2 is negative.

The line for y\geq x+2 is dotted instead of solid.

The graph for y\geq x+2 is shaded above the line.

1

Is (1,3) a solution to the inequality? y\geq x+2?

yes

no

Let's make some conclusions...

1

If the symbols in an inequality are < or > will the line on the graph be solid or dotted?

1

If the symbols in an inequality are \leq or \geq will the line on the graph be solid or dotted?

1

If the symbols in an inequality are < or \leq will the graph be shaded above or below the line?

1

If the symbols in an inequality are > or \geq will the graph be shaded above or below the line?

1

What does the shaded region on a graph represent?

4

Match each graph with its inequality.

y<-x+1
y\leq -x+1
y>-x+1
y\geq -x+1

Use this chart to fill in the bottom left graphs on your notes sheet.

1

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!

(-3,5)

(2,-2)

(3,5)

(5,-3)

1

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!

(-2,4)

(-4,4)

(1,-2)

(1,6)

Now it's time for the main event...graphing SYSTEMS of inequalities!!!

Check out the process below. I also do two examples in the 5 minute video below. When you're ready to try some, turn your notes sheet over and start graphing!

Still unsure? Watch this 5 minute video.

Ask me to check your graphs in #24 and #25 (or compare them with a partner) before you submit!

Systems of Inequalities

Let's make some conclusions...

Use this chart to fill in the bottom left graphs on your notes sheet.

Now it's time for the main event...graphing SYSTEMS of inequalities!!!

Systems of Inequalities

Type the equation of the line in the graph below. y=mx+b

Type in a point (x,y) that lies on this line.

Does(1,3) lie on this line?

Is (1,3) a solution to the equation y=x+2?

Type y<x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#6) y<x+2.

Is (1,3) a solution to the inequality? y<x+2?

Notice in the example below, when = changes to < the point on the line is no longer a solution.

Type y\le x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#9) y\le x+2.

Is (1,3) a solution to the inequality? y\le x+2?

Notice in the example below, when = changes to \leq the point on the line is still a solution!

Type y> x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#12) y>x+2.

Is (1,3) a solution to the inequality? y> x+2?

Type y\geq x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#15) y\geq x+2.

Is (1,3) a solution to the inequality? y\geq x+2?

Let's make some conclusions...

If the symbols in an inequality are < or > will the line on the graph be solid or dotted?

If the symbols in an inequality are \leq or \geq will the line on the graph be solid or dotted?

If the symbols in an inequality are < or \leq will the graph be shaded above or below the line?

If the symbols in an inequality are > or \geq will the graph be shaded above or below the line?

What does the shaded region on a graph represent?

Match each graph with its inequality.

Use this chart to fill in the bottom left graphs on your notes sheet.

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.*Clearly show if your line is dotted or solid!*Clearly show shading above or below the line!

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.*Clearly show if your line is dotted or solid!*Clearly show shading above or below the line!

Now it's time for the main event...graphing SYSTEMS of inequalities!!!

Type the equation of the line in the graph below. y=mx+b

Type in a point (x,y) that lies on this line.

Does(1,3) lie on this line?

Is (1,3) a solution to the equation y=x+2?

Type y<x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#6) y<x+2.

Is (1,3) a solution to the inequality? y<x+2?

Notice in the example below, when = changes to < the point on the line is no longer a solution.

Type y\le x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#9) y\le x+2.

Is (1,3) a solution to the inequality? y\le x+2?

Notice in the example below, when = changes to \leq the point on the line is still a solution!

Type y> x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#12) y>x+2.

Is (1,3) a solution to the inequality? y> x+2?

Type y\geq x+2 in the textbox below to see its graph.Then sketch an accurate graph on your notes sheet & answer the questions below it.

Select EVERYTHING that's true about the graph of the inequality (#15) y\geq x+2.

Is (1,3) a solution to the inequality? y\geq x+2?

If the symbols in an inequality are < or > will the line on the graph be solid or dotted?

If the symbols in an inequality are \leq or \geq will the line on the graph be solid or dotted?

If the symbols in an inequality are < or \leq will the graph be shaded above or below the line?

If the symbols in an inequality are > or \geq will the graph be shaded above or below the line?

What does the shaded region on a graph represent?

Match each graph with its inequality.

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.*Clearly show if your line is dotted or solid!*Clearly show shading above or below the line!

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.*Clearly show if your line is dotted or solid!*Clearly show shading above or below the line!

Type y<x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y\le x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y> x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y\geq x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!

Type y<x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y\le x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y> x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Type y\geq x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
Clearly show if your line is dotted or solid!
Clearly show shading above or below the line!