Question

1. write the equation of the line that passes through (-6, -10) with slope 2.

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=-6$, $y_1 = - 10$ and $m = 2$.

Step2: Substitute values into point - slope form

Substitute $x_1=-6$, $y_1=-10$ and $m = 2$ into the point - slope formula:
$y-(-10)=2(x - (-6))$
Simplify the left - hand side and the right - hand side:
$y + 10=2(x + 6)$

Step3: Expand and simplify to slope - intercept form (optional, but to get a more standard form)

Expand the right - hand side: $y+10 = 2x+12$
Subtract 10 from both sides: $y=2x + 12-10$
$y=2x+2$
We can also write it in standard form $Ax+By = C$. Subtract $y$ and 2 from both sides: $2x-y=-2$

Answer:

The equation of the line is $y = 2x+2$ (or $2x - y=-2$)