Unit 2 Review Part 2

Not only do we have positive and negative slopes, we also have slopes that are 0 or undefined.

Positive Slope

Negative Slope

SLOPE-INTERCEPT FORM

The previous formula we used has a name and it is called slope-intercept form. This basic form that we use tell us two things about the data that accompanies it.

Remember, an equation is denoted with y and a function is f(x).

These are the two way you may see it and we are already familiar with the first one. Again, m stands for the slope (rate of change) and b stands for the starting value. The starting value is also the y-intercept of the graph. This is where the graph crosses the y-axis.

In order to put something in slope-intercept form, we need to know the above mentioned parts. That means we must determine the slope and intercept.

This is shown in the images on the right.

PARALLEL LINES

Parallel lines are lines that have the same slope but different y-intercepts. We may be given a question where we are asked to determine the equation of a line that is parallel to another that passes through a specific point. Below is an example of a problem and how it is worked.

We determine the value of the new slope first which is the same value since parallel lines have the same slope. *Then we use the slope-intercept formula to find the new y-intercept by substituting the slope and the point the new line passes through. This will give us the new line's equation.

On Desmos

If you want to try these on desmos, you still have to know about the slopes of parallel lines. You can plot the point the new line passes through and use the slope to determine what the y-intercept would be.

Perpendicular Lines

Perpendicular lines are worked almost like parallel lines except the slopes are different. They are opposite reciprocals. To get the opposite reciprocal, you will flip the positions of the numerator and denominator. This means that if the slope was 4, the perpendicular slope would be -1/4.

If the slope of the original line is -2, the perpendicular slope would be 1/2.

Below is an example of how it is worked to find the new equation of a perpendicular line that passes through a point.

You do the same steps as parallel lines. Substitute the new slope and the point the line passes through and solve for b.

On Desmos

If looking to do this on desmos, you work it like the parallel lines. Plot the new point the line passes through and use the new slope to find the y-intercept.