Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$y=x+2$
The equation of a line in the point-slope form is the following: $y-y_1=m(x-x_1)$, where $m$ is the slope and the point $(x_1,y_1)$ is on the graph. In order to determine the equation of a line, we have to calculate the slope. For this, we can use the rule, that the product of the slopes of two perpendicular lines equals $-1$. Here, a perpendicular line is $y=-x$. In this form, the slope can be seen as the coefficient of $x$, which is $-1$. Therefore our line's slope $m$ can be calculated as: $m\times(-1)=-1$ $m=\dfrac{-1}{-1}=1$ Therefore, using the point $(-1, 1)$ and the slope $1$, the equation can be written as: $y-1=1(x-(-1))$ $y-1=x+1\\ y=x+1+1\\ y=x+2$