Question

When a linear function is graphed on the coordinate plane, the line intersects the x-axis at (1,0), and the rate of change is 3.Which two points define the linear function?A. (2,3), (3, 12)B.(2, 3), (3,9)С.(2, 3). (3, 10)D.(2, 3), (3,6)

Answer 1

The information we have is:

The x-intercept is at (1,0).

And the rate of change is 3.

Step 1. Identify the x-intercept. A graph can help us identify the point (1,0)

Now, we use the rate of change to find more points of the line.

Step 2. The rate of change is defined as follows:

`\text{rate of change=}\frac{change\text{ in y}}{change\text{ in x}}`

Since in this case, the rate of change is 3:

`\text{rate of change=3}`

If we represent it in a fraction form:

`\text{rate of change=}(3)/(1)`

And compare it to the definition of the rate of change, we can see the following:

`\begin{gathered} \text{change in y = 3} \\ \text{change in x =1} \end{gathered}`

Step 3. Identify points of the line using the x-intercept and the rate of change.

We start at the point (1,0) and the next point will be at 3 above in the x-direction and 1 to the right in the x-direction:

And now, from (2,3) the next point will also be 3 above in the y-direction and 1 to the right in the x-direction:

We have found two points that define the linear function:

(2,3) and (3,6)