Instructions

In this exercise, we are given the graph or image of a line for which we must find the equation in the form y = mx + b.

Since "b" is the y-intercept and "m" is the slope, which of course is rise over run or change in y over change in x, we can easily find the equation once we figure out how much we must rise and run to get to another point on the line with integer coefficients.

Example 1

Example 2

Notice how a line with a positive slope leans to the right and a line with a negative slope leans towards the left.

If b = 0, the line goes through the origin, so y = 3x looks like this:

Practice

1) Write the equation of the line shown in y = mx + b form.

Solutions

a) since 4/6 = 2/3, the slope is 2/3 and the y-intercept is – 4 so the equation is .

b) slope = – 4/3, and the y-intercept is 0 so the equation is .

c) slope = – 7/8, and the y-intercept is 7 so the equation is .

d) slope = 4/3, and the y-intercept is 2 so the equation is .

e) slope = – 1/7, and the y-intercept is 6 so the equation is .

f) slope = 1, and the y-intercept is 0 so the equation is .

( Analytic Geometry MathRoom Index )