Question

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

Answer 1

Answer:

The x-intercept of the line is the point (12,0)

Step-by-step explanation:

step 1

Find the slope of the lime

Take the points

(22,36) and (32,72)

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

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

substitute the values

$m=\frac{72-36}{32-22}$

$m=\frac{36}{10}$

$m=3.6$

step 2

Find the equation of the line in point slope form

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

we have

$m=3.6$

$point (22,36)$

substitute

$y-36=3.6(x-22)$

step 3

Find the x-intercept

we know that

The x-intercept of a line is the value of x when the value of y is equal to zero

so

For y=0

substitute in the equation and solve for x

$0-36=3.6(x-22)$

$0-36=3.6x-79.2$

$3.6x=79.2-36$

$3.6x=43.2$

$x=12$

therefore

The x-intercept of the line is the point (12,0)