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

Answer:

$x_2 - x_1 = 1$ gives $y_2 - y_1 = 4$

Step-by-step explanation:

Given

$y = 4x$

$(x_1,x_2) = (x,x+1)$

Required

Show that the y values increases by 4 for $x_2 - x_1 = 1$

We have:

$y = 4x$

For $x_1 = x$

$y_1 = 4x_1$

Substitute $x_1 = x$

$y_1 = 4x$

For $x_2 = x + 1$

$y_2 = 4x_2$

Substitute $x_2 = x + 1$

$y_2 = 4(x+1)$

$y_2 = 4x+4$

So, we have:

$y_2 = 4x+4$

$y_1 = 4x$

Subtract $y_1$ from $y_2$

$y_2 - y_1 = 4x + 4 - 4x$

Collect like terms

$y_2 - y_1 = 4x - 4x+ 4$

$y_2 - y_1 = 4$

Hence:

$x_2 - x_1 = 1$ gives $y_2 - y_1 = 4$

i.e. an increment of 4