Question

a line passes through the point (-3, 8) and has a slope of 2. write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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. We know that the point $(x_1,y_1)=(-3,8)$ and the slope $m = 2$. Substitute these values into the point - slope form:
$y - 8=2(x - (-3))$ which simplifies to $y - 8=2(x + 3)$

Step2: Convert to slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We need to simplify the equation $y - 8=2(x + 3)$ to get it in the form $y=mx + b$.
First, distribute the 2 on the right - hand side: $y - 8=2x+6$.
Then, add 8 to both sides of the equation to solve for $y$: $y=2x + 6+8$.
Simplify the right - hand side: $y=2x+14$

Answer:

$y = 2x+14$