Question

A linear function is given by the equation y=4x
. Using the points x
and x+1
, show that the y-values increase by 4 between any two points separated by x2−x1=1
.

Answer 1

put it in a tadel

Answer 2

Let's plug in the points x and x+1 into the equation y=4x:

For x, y = 4x = 4(x) = 4x
For x+1, y = 4(x+1) = 4x + 4

The difference in y-values between the two points is:
4x + 4 - 4x = 4

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

Answer 3

Let x1 and x2 be two points such that x2 - x1 = 1.

For x1, y1 = 4(x1) = 4x1
For x2, y2 = 4(x2) = 4x2

The difference in y-values between the two points is:
y2 - y1 = 4x2 - 4x1 = 4(x2 - x1) = 4(1) = 4

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