Introductory Algebra for College Students (7th Edition)

The point-slope form of the equation for this line is: $$y + 1 = -2(x - 3)$$ The slope-intercept form of the equation for this line is: $$y = -2x + 5$$
We use the slope and the point given to write the equation of the line in point-slope form: $$y - y_{1} = m(x - x_{1}$$ Plug in the information given into this equation: $$y - (-1) = -2(x - 3)$$ Simplify the equation on the left-hand side: $$y + 1 = -2(x - 3)$$ Now, we find the y-intercept by plugging in $0$ for $x$ and then solving for $y$: $$y + 1 = -2(0 - 3)$$ Evaluate parentheses first: $$y + 1 = -2(-3)$$ Multiply right side of the equation: $$y + 1 = 6$$ Subtract $1$ from both sides to solve for $y$: $$y = 5$$ Now that we have the y-intercept, we can plug it into the slope-intercept equation, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept: $$y = -2x + 5$$