Geometry 3-7 Complete Lesson: Equations of Lines in the Coordinate Plane

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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Draggable item		Corresponding Item
Hill B		Easiest
Hill C		Intermediate
Hill A		Difficult

Draggable item		Corresponding Item
		Positive slope
		Negative slope
		Zero slope
		Undefined slope

Draggable item		Corresponding Item
lining		ADJECTIVE
linear		NOUN
line		VERB (present-tense)

Draggable item		Corresponding Item
Hill B		Easiest
Hill C		Intermediate
Hill A		Difficult

Draggable item		Corresponding Item
		Positive slope
		Negative slope
		Zero slope
		Undefined slope

Geometry 3-7 Complete Lesson: Equations of Lines in the Coordinate Plane

Geometry 3-7 Complete Lesson: Equations of Lines in the Coordinate Plane

Solve It! Ski resorts use steepness to rate the difficulty of their hills. The steeper the hill, the higher the difficulty rating. Shown are stretches of three new hills at a particular resort. Which hill gets which rating?

Take Note: Define slope. You may use the canvas to help illustrate your description.

Take Note: Describe how you can find the slope of a line if you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 1 Got It? What is the slope of line a?

Problem 1 Got It? What is the slope of line c? Enter only a number.

Take Note: On the canvas, sketch an example of a line that has positive slope.

Take Note: Write the general equation for slope-intercept form. Enter only the equation, with no spaces.

Problem 2 Got It? Graph the equation on the canvas. Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Got It? Graph the equation on the canvas. Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Extension: Graph both equations on the same plane using the embedded Desmos utility. Zoom and pan your graph to establish an appropriate viewing window.

Problem 3 Got It?

Problem 3 Got It?

Take Note: Summarize the process of writing the equation of a line in slope-intercept form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Take Note: Summarize the process of writing the equation of a line in point-slope form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 4 Got It? Graph both of the equations below, created from Problem 4 and its Got It, on the same plane. Zoom and pan your graph to establish an appropriate viewing window.

Take Note: Match each graph with its slope.

Problem 5 Got It?

Problem 5 Got It?

What is an equation of a line with slope 8 and y-intercept 10?

Compare and Contrast: Graph the equations on the canvas. Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Error Analysis: A classmate found the slope of the line passing through (8, -2) and (8, 10), as shown here. Describe your classmate's error.

Find the correct slope of the line passing through the given points.

Review Lesson 2-5: Categorize each statement based on the property it demonstrates.

Review Lesson 3-7: Find the slope of the line passing through the points.

Review Lesson 3-7: Find the slope of the line passing through the points.

Vocabulary Review: Categorize each statement on the left as true or false.

Use Your Vocabulary: Complete each statement on the right with the appropriate word from the left. Use each word only once.

Use Your Vocabulary: Match each word on the left with its part of speech on the right.

Reflection: Math Success

Solve It! Ski resorts use steepness to rate the difficulty of their hills. The steeper the hill, the higher the difficulty rating. Shown are stretches of three new hills at a particular resort. Which hill gets which rating?

Take Note: Define slope. You may use the canvas to help illustrate your description.

Take Note: Describe how you can find the slope of a line if you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 1 Got It? What is the slope of line a?

Problem 1 Got It? What is the slope of line c? Enter only a number.

Take Note: On the canvas, sketch an example of a line that has positive slope.

Take Note: On the canvas, sketch an example of a line that has negative slope.

Take Note: On the canvas, sketch an example of a line that has zero slope.

Take Note: On the canvas, sketch an example of a line that has undefined slope.

Take Note: Write the general equation for slope-intercept form. Enter only the equation, with no spaces.

Take Note: Write the general equation for point-slope form. Enter only the equation, with no spaces. Hints: You may use the subscript button on the math input keyboard or the underscore key to initiate subscript. Use the right arrow to exit subscript.

Problem 2 Got It? Graph the equation on the canvas. Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Got It? Graph the equation on the canvas. Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Extension: Graph both equations on the same plane using the embedded Desmos utility. Zoom and pan your graph to establish an appropriate viewing window.

Problem 3 Got It?

Problem 3 Got It?

Take Note: Summarize the process of writing the equation of a line in slope-intercept form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Take Note: Summarize the process of writing the equation of a line in point-slope form when you know the coordinates of two points on the line. You may use the canvas to help illustrate your description.

Problem 4 Got It? Graph both of the equations below, created from Problem 4 and its Got It, on the same plane. Zoom and pan your graph to establish an appropriate viewing window.

Take Note: Match each graph with its slope.

Problem 5 Got It?

Problem 5 Got It?

What is an equation of a line with slope 8 and y-intercept 10?

Compare and Contrast: Graph the equations on the canvas. Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Error Analysis: A classmate found the slope of the line passing through (8, -2) and (8, 10), as shown here. Describe your classmate's error.

Find the correct slope of the line passing through the given points.

Review Lesson 2-5: Categorize each statement based on the property it demonstrates.

Review Lesson 3-7: Find the slope of the line passing through the points.

Review Lesson 3-7: Find the slope of the line passing through the points.

Vocabulary Review: Categorize each statement on the left as true or false.

Use Your Vocabulary: Complete each statement on the right with the appropriate word from the left. Use each word only once.

Use Your Vocabulary: Match each word on the left with its part of speech on the right.

Reflection: Math Success

Take Note: On the canvas, sketch an example of a line that has negative slope.

Take Note: On the canvas, sketch an example of a line that has zero slope.

Take Note: On the canvas, sketch an example of a line that has undefined slope.

Take Note: Write the general equation for point-slope form. Enter only the equation, with no spaces. Hints: You may use the subscript button on the math input keyboard or the underscore key to initiate subscript. Use the right arrow to exit subscript.

Solve It! Ski resorts use steepness to rate the difficulty of their hills. The steeper the hill, the higher the difficulty rating. Shown are stretches of three new hills at a particular resort.
Which hill gets which rating?

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Compare and Contrast: Graph the equations on the canvas.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Solve It! Ski resorts use steepness to rate the difficulty of their hills. The steeper the hill, the higher the difficulty rating. Shown are stretches of three new hills at a particular resort.
Which hill gets which rating?

Take Note: Write the general equation for point-slope form. Enter only the equation, with no spaces.
Hints: You may use the subscript button on the math input keyboard or the underscore key to initiate subscript. Use the right arrow to exit subscript.

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Problem 2 Got It? Graph the equation on the canvas.
Be sure to include all relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Compare and Contrast: Graph the equations on the canvas.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Take Note: Write the general equation for point-slope form. Enter only the equation, with no spaces.
Hints: You may use the subscript button on the math input keyboard or the underscore key to initiate subscript. Use the right arrow to exit subscript.