Question

Finding the Equation of a Line from a Table
What is the equation of the line with points represented in the table?

A 2-column table with 3 rows. Column 1 is labeled x with entries negative 8, 4, 8. Column 2 is labeled y withentries 6, negative 3, negative 6.

What can you conclude about the line represented in the table? Select all that apply.

Using either slope-intercept or point-slope forms will result in different equations.
Using either slope-intercept or point-slope forms will result in the same equation.
The slope is Negative four-thirds.
The slope is Negative four-thirds.
The y-intercept is 2.
The y-intercept is 0.

Answer 1

First find the slope:
m = (−3 − 6) / (4 − (−8)) = (−9) / 12 = −3/4
(You get the same slope −3/4 between any pair of the given points.)

Equation using point-slope with (4,−3):
y + 3 = (−3/4)(x − 4) ⇒ y = (−3/4)x.

So the true statements are:
- Using either slope-intercept or point-slope forms will result in the same equation. (True)
- The slope is −3/4. (True)
- The y-intercept is 0. (True)

The other listed choices (different equations; slope −4/3; y-intercept 2) are false.