Question

This table gives a few (x,y) pairs of a line on the coordinate plane

Answer 1

Answer:

(22, 0)

Step-by-step explanation:  

Answer 2

Answer:

The x-intercept is the point (22,0)

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take the points

(-38,40) and (-23,30)

substitute the given values

$m=\frac{30-40}{-23+38}$

$m=\frac{-10}{15}$

$m=-\frac{2}{3}$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{2}{3}$

$point\ (-8,20)$

substitute

$y-20=-\frac{2}{3}(x+8)$

step 3

Find the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$0-20=-\frac{2}{3}(x+8)$

solve for x

$-20=-\frac{2}{3}x-\frac{16}{3}$

Multiply by 3 both sides

$-60=-2x-16$

$2x=60-16\\2x=44\\x=22$

therefore

The x-intercept is the point (22,0)