Question

Determine the intercepts of the line that correspond to the following table of values. x y 4 0 12 5 20 10

Answer 1

Let

A(4,0)

B(12,5)

C(20,10)

we know that

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

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

The point A(4,0) is the x-intercept of the line

Find the slope AB

m=(y2-y1)/(x2-x1)

mAB=(5-0)/(12-4)--------> mAB=5/8

with the slope m and the point A(4,0) find the equation of the line

y-y1=m*(x-x1)----------> y-0=(5/8)*(x-4)-------> y=(5/8)x-2.5-----> y=0.625x-2.5

Find the y-intercept

For x=0

y=0.625*0-2.5---------> y=-2.5

the y-intercept is the point (0,-2.5)

therefore

the answer is

the x-intercept is the point (4,0)

the y-intercept is the point (0,-2.5)

see the attached figure to better understand the problem