Writing Linear Equations – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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If you only know a couple points on a line, how can you write a linear equation into slope-intercept form, y = mx + b?

A couple points on a line is all you need. To calculate the slope, decide which of two points will be the first ordered pair and the second, and then plug the x and y-values into the slope formula. Alternatively, you may be able to look at the graph and determine the rise over the run between any two points – the change in the height divided by the change in the width.

After you have figured out the slope, the m-value in the slope-intercept form, you can figure out the b-value, the y-intercept. Into the slope intercept form you have written so far, use the coordinates for one point on the line and plug in those values for x and y.

To calculate the y-intercept, isolate the b-value. There are some other shortcuts to help you write linear equations. If lines are parallel, they have the same slope but different y-intercepts. If the lines are perpendicular, the slopes will have a negative inverse (negative reciprocal) relationship, and the products of the two slopes will be -1. This is sort of hard to describe using words. Maybe you had better watch this video on the topic of writing linear equations.

Write equations of the line.


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Exercises in this Practice Problem
Determine the linear equation in slope-intercept form.
Explain how to set up an equation for a parallel line.
Find the equation of the line that is perpendicular to $y=\frac12 x+2$ and passes through $B(7,5)$.
Decide which equations are represented by the given graphs.
Identify the lines that are parallel or perpendicular to the orange line.
Write the equations for the given graphs in different forms.