Question

write the linear equation that gives the rule for this table.
x | y
-36 | -68
-17 | -49
2 | -30
21 | -11
write your answer as an equation with y first, followed by an equals sign.
submit

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(-36, -68)$ and $(-17, -49)$.
$m = \frac{-49 - (-68)}{-17 - (-36)} = \frac{-49 + 68}{-17 + 36} = \frac{19}{19} = 1$.

Step2: Use point-slope form to find the equation

Point-slope form is $y - y_1 = m(x - x_1)$. Let's use the point $(2, -30)$ and $m = 1$.
$y - (-30) = 1(x - 2)$
$y + 30 = x - 2$

Step3: Simplify to slope-intercept form

Subtract 30 from both sides: $y = x - 2 - 30$
$y = x - 32$

Answer:

$y = x - 32$