Changing the value of b will make the graph go up or down.
Work Step by Step
This is the case because b is the y-intercept of the graph. We prove this by thinking that at the y-intercept, the x-coordinate is 0, so when we plug in zero into the equation: y=mx+b, we get y=b. Therefore, b is the y-intercept. Now changing b (aka. the y-intercept) will make the graph move vertically because that will change when the graph hits the y axis.