@puzzlevai.bsky.socialLift a straight line without rotating it. What changes?
y = mx becomes y = mx + b.
The value b changes the line’s starting height, while m—and therefore the slope—remains unchanged. Same steepness, different y-intercept.
8.EE.6 | Math 8
@puzzlevai.bsky.socialWhy does a straight line keep the same slope?
The right triangles formed along the line are similar. Their rise and run increase by the same scale factor, so the ratio rise ÷ run remains constant.
That constant ratio is slope.
8.EE.6 | Math 8
@puzzlevai.bsky.socialWhich system has the greater unit rate?
Both rise for the same amount of time, but the gold system gains more. Therefore, its unit rate is greater.
For a proportional relationship, unit rate is also the slope of its graph and the value of m in y = mx.