Question

what is an equation of the line that passes through the points (-6, -1) and (-4, 2)?

Explanation:

Step1: Calculate slope $m$

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-6,-1)$ and $(x_2,y_2)=(-4,2)$:
$m=\frac{2-(-1)}{-4-(-6)}=\frac{3}{2}$

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-6,-1)$:
$y-(-1)=\frac{3}{2}(x-(-6))$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y+1=\frac{3}{2}(x+6)$
$y+1=\frac{3}{2}x + 9$
$y=\frac{3}{2}x + 8$

Answer:

$y=\frac{3}{2}x + 8$ (or in standard form: $3x-2y=-16$)