$y = 2x + 9$
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.