A linear function is given by the equation y=4x. Using the points x and x+1, 0 show that the y-values increase by 4 between any two points separated by x2−x1=1

Question

A linear function is given by the equation y=4x. Using the points x and x+1, 0 show that the y-values increase by 4 between any two points separated by x2−x1=1

please help

Answer 1

let f(x) = 4x

f(x+1) = 4(x+1) = 4x + 4

so the difference between the y values for consecutive x's
y₂ - y₁
= f(x+1) - f(x)
= 4x + 4 - 4x
= 4
what does my result show?

Answer 2

To show that the y-values increase by 4 between any two points separated by x2 - x1 = 1, we can substitute the given points x and (x+1) into the equation y = 4x and compare their y-values.

Let's start with the first point, x.

Substitute x into the equation:
y = 4x
y = 4(x)

Now, let's consider the second point, x+1.

Substitute (x+1) into the equation:
y = 4(x+1)
y = 4x + 4

Now, let's calculate the difference between the y-values of the two points:
Difference = (4x + 4) - (4x)
Difference = 4x + 4x + 4 - 4x
Difference = 4x + 4x - 4x + 4
Difference = 4

We observe that the difference between the y-values of the two points is 4, which confirms that the y-values increase by 4 between any two points separated by x2 - x1 = 1.