Question

This table gives a few (x,y) pairs of a line in the coordinate plane.(34, -52), (51,-65), (68, -78).What is the y-intercept of the line?

Answer 1

(0,-26)

Explanation:

Write the equation of the line in the slope-intercept form:

1. The slope of the line is

`(-65-(-52))/(51-34)=-(13)/(17)`

2. The equation of the line is

`y-(-52)=-(13)/(17)(x-34)\\ \\y+52=-(13)/(17)x+26\\ \\y=-(13)/(17)x-26`

Now, find the y-intercept, substitute x = 0:

`y=-(13)/(17)\cdot 0-26\\ \\y=-26`