Question

What is the function rule for the line?

f(x)=23x−2

f(x)=32x+2

f(x)=32x−2

f(x)=−23x−2

Answer 1

`f(x)=(2)/(3)-2`

First option is correct.

Explanation:

The intercept form of a line is given by

`(x)/(a)+(y)/(b)=1`

Here a is the x-intercept and b is the y-intercept.

From the given graph,

x-intercept = 3

y-intercept = -2

Hence, we have

a = 3 and b = -2

Substituting these values in above equation

`(x)/(3)+(y)/(-2)=1\\\\(x)/(3)-(y)/(2)=1\\\\(y)/(2)=(x)/(3)-1\\\\y=(2)/(3)-2`

Hence, the function rule for the line is given by

`f(x)=(2)/(3)-2`

First option is correct.

Answer 2

Find the slope of the line by using two points on the line.

Using (0,-2) and (3,0)

The slope is the change in Y over the change in x:

Slope = (0 - -2) / (3-0) = 2/3

The y intercept is where the line crosses Y at = 0, from the picture when X is 0 the line crosses at -2.

The equation becomes 2/3x -2

The answer is: f(x)=2/3x−2