Question

find the equation of this line. y = -\frac{1}{?}x+

Explanation:

Step1: Find two points on the line

The line passes through (-6, -2) and (0, -3).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-6,-2)$ and $(x_2,y_2)=(0,-3)$. Then $m=\frac{-3-(-2)}{0 - (-6)}=\frac{-3 + 2}{6}=-\frac{1}{6}$.

Step3: Find the y - intercept $b$

The equation of a line is $y=mx + b$. We know $m =-\frac{1}{6}$ and the line passes through (0, -3). Substituting $x = 0$ and $y=-3$ into $y=-\frac{1}{6}x + b$, we get $-3=-\frac{1}{6}(0)+b$, so $b=-3$.

Answer:

$y =-\frac{1}{6}x-3$