Question

Recall that we can compare the vertical distance between any two points on the same vertical line to measure verticalchange. In the same way, the horizontal distance between any two points on the same horizontal line will measurehorizontal change.Suppose the linear function y = ax + b undergoes a horizontal change of 5 units. This is equivalent to what verticalchange?A) a vertical change of 5 + b unitsB)a vertical change of 5a + b unitsC)a vertical change of 5 unitsD)a vertical change of 5/a unitsE)a vertical change of 5a units

Answer 1

Given the linear function:

y = ax + b

And it undergoes a horizontal shift of 5 units

Let the original line be f(x) and the new line be g(x)

g(x) = f(x - 5)

The vertical change will be the horizontal change times a, using the definition of slope.

Thus, since the horizontal change here is 5 units, the vertical change is 5a units

ANSWER:

E) a vertical change of 5a units