Question

a line passes through the point (-2,8) and has a slope of 5. write an equation in slope - intercept form for this line.

Explanation:

Step1: Recall 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 know that $m = 5$ and the line passes through the point $(-2,8)$. Substitute $x=-2$, $y = 8$ and $m = 5$ into the equation $y=mx + b$.
So we have $8=5\times(-2)+b$.

Step2: Solve for $b$

First, calculate $5\times(-2)=- 10$. Then the equation becomes $8=-10 + b$.
To solve for $b$, add 10 to both sides of the equation: $b=8 + 10=18$.

Step3: Write the equation

Now that we know $m = 5$ and $b = 18$, substitute these values into the slope - intercept form $y=mx + b$.
We get $y = 5x+18$.

Answer:

$y = 5x + 18$