Question

a line passes through the point (-1, 1) and has a slope of 8.
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. Here, $x_1=- 1$, $y_1 = 1$ and $m = 8$. Substitute these values into the point - slope form:
$y-1=8(x - (-1))$ which simplifies to $y - 1=8(x + 1)$

Step2: Expand and convert to slope - intercept form

Slope - intercept form is $y=mx + b$. Expand the right - hand side of $y - 1=8(x + 1)$:
$y-1=8x+8$
Then, add 1 to both sides of the equation:
$y=8x + 8+1$
$y=8x+9$

Answer:

$y = 8x+9$