Question

complete the equation of the line through (-6, -5) and (-4, -4). use exact numbers. y =

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-6, -5)$ and $(x_2, y_2) = (-4, -4)$. Then $m = \frac{-4 - (-5)}{-4 - (-6)} = \frac{-4 + 5}{-4 + 6} = \frac{1}{2}$.

Step2: Use point - slope form to find the equation

The point - slope form is $y - y_1 = m(x - x_1)$. Using the point $(-6, -5)$ and $m=\frac{1}{2}$, we have $y - (-5)=\frac{1}{2}(x - (-6))$. Simplify this: $y + 5=\frac{1}{2}(x + 6)$. Distribute the $\frac{1}{2}$: $y + 5=\frac{1}{2}x+3$. Subtract 5 from both sides: $y=\frac{1}{2}x+3 - 5=\frac{1}{2}x - 2$.

Answer:

$\frac{1}{2}x - 2$