Question

write the linear equation that gives the rule for this table.

x | y
3 | -16
4 | -22
5 | -28
6 | -34

write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (3, -16) and (4, -22):
$m = \frac{-22 - (-16)}{4 - 3} = \frac{-22 + 16}{1} = \frac{-6}{1} = -6$

Step2: Use point - slope form to find the equation

The point - slope form is $y - y_1 = m(x - x_1)$. Let's use the point (3, -16) and $m=-6$:
$y - (-16)=-6(x - 3)$
Simplify the left side: $y + 16=-6(x - 3)$
Expand the right side: $y + 16=-6x+18$
Subtract 16 from both sides: $y=-6x + 18 - 16$
Simplify: $y=-6x + 2$

Answer:

$y=-6x + 2$