Question

what linear equation describes the following set of points?
{(-12, 7), (4, -5), (12, -11)}
$y = -\frac{3}{4}x - 2$
$y = -\frac{3}{4}x + 2$
$3x + 4y = -2$
$y = \frac{4}{3}x - 2$

Explanation:

Step1: Test first point in Option1

Substitute $x=-12, y=7$ into $y = -\frac{3}{4}x - 2$:
$7 = -\frac{3}{4}(-12) - 2 = 9 - 2 = 7$ (valid)

Step2: Test second point in Option1

Substitute $x=4, y=-5$ into $y = -\frac{3}{4}x - 2$:
$-5 = -\frac{3}{4}(4) - 2 = -3 - 2 = -5$ (valid)

Step3: Test third point in Option1

Substitute $x=12, y=-11$ into $y = -\frac{3}{4}x - 2$:
$-11 = -\frac{3}{4}(12) - 2 = -9 - 2 = -11$ (valid)

Step4: Verify other options (optional)

For Option2: $7 = -\frac{3}{4}(-12)+2=11$ (invalid)
For Option3: $3(-12)+4(7)=-36+28=-8
eq-2$ (invalid)
For Option4: $7 = \frac{4}{3}(-12)-2=-18$ (invalid)

Answer:

$y = -\frac{3}{4}x - 2$