Question

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

-56 66
-42 58
-28 50
What is the y-intercept of the line?

Answer 1

The y-intercept of the line is 34.

Explanation:

There are few points on the z-y plane through which a straight line passes.

The points are (-56,66), (-42,58) and (-28,50).

Now, take the first two points to get the equation of the straight line.

The equation is
`(y - 58)/(58 - 66) = (z - (-42))/(-42 - (- 56))`

⇒
`(y - 58)/(- 8) = (z + 42)/(14)`

⇒ 14(y - 58) = - 8(z + 42)

⇒
`y - 58 = - (8)/(14)z - 24`

⇒
`y =  - (8)/(14)z + 34`

This equation is in slope-intercept form.

Hence, the y-intercept of the line is 34. (Answer)