Answer
$y = 2x + 9$
Work Step by Step
We are given the line $y - 5 = 2(x + 2)$.
This equation is in point-slope form, which is given by the formula:
$y - y_1 = m(x - x_1)$,
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
However, we want this line in slope-intercept form.
The first thing we want to do is use the distributive property to get rid of the parentheses:
$y - 5 = 2(x) + 2(2)$
Multiply to simplify the equation:
$y - 5 = 2x + 4$
The slope-intercept form is given by the equation:
$y = mx + b$,
where $m$ is the slope of the line and $b$ is the y-intercept of the line.
Therefore, with the slope-intercept form, we need to isolate $y$. We do this by adding $5$ to each side of the equation:
$y - 5 + 5 = 2x + 4 + 5$
Add to simplify:
$y = 2x + 9$
This line is now rewritten in slope-intercept form.
