A linear function is given by the equation y=4x . Using the points x

Question

and x+1
, show that the y-values increase by 4 between any two points separated by x2−x1=1

Answer 1

Given the linear function y = 4x, we want to show that the y-values increase by 4 between any two points separated by x2 - x1 = 1.

Let's choose two points x and x+1:

Point 1: x
y1 = 4x

Point 2: x+1
y2 = 4(x+1)
y2 = 4x + 4

Now, let's find the difference in y-values between these two points:
y2 - y1 = (4x + 4) - 4x
y2 - y1 = 4

Therefore, the y-values increase by 4 between any two points separated by x2 - x1 = 1, as shown.