Recognizing Linear Functions

a

Let's start by marking the points in a coordinate plane.

Now we need to draw a line that goes through both points. We need to keep in mind that the line should continue before and after the points.

b

Now that we have the line drawn we can find its rate of change by determining the change in $x,$ $Δ x,$ and change in $y,$ $Δ y .$

The rate of change of the line can be determined by dividing the

Δ y

by

Δ x .

rate of change = \frac{Δ y}{Δ x}

In the graph we can see that

Δ x = 2

and

Δ y = 2 .

rate of change = \frac{Δ y}{Δ x}

Δ x = 2

,

Δ y = 2

rate of change = \frac{2}{2}

CalcQuotCalculate quotient

rate of change = 1

Thus, the line's rate of change is

1 .

Recognizing Linear Functions 1.5 - Solution