## Precalculus (6th Edition) Blitzer

For the point $\left( 4,0 \right)$, the equation is $y-0=\frac{1}{2}\left( x-4 \right)$ and for the point $\left( 0,-2 \right)$, the equation is $y+2=\frac{1}{2}\left( x-0 \right)$. The slope intercept form of the line is $y=\frac{1}{2}x-2$.
The points through which the line passes are given by $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$. Here, these points are $\left( 4,0 \right)$ and $\left( 0,-2 \right)$. Therefore, the slope of the line is $m=\frac{-2-0}{0-\left( 4 \right)}=\frac{-2}{-4}=\frac{1}{2}$. The slope of the line is $\frac{1}{2}.$ The equation of the line in point-slope form can be calculated by using the formula $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$ …………………………………………….….. (2) The line passes through two points, so there can be two equations of the line in point- slope form using equation (2). For the point $\left( 4,0 \right)$ , the equation is $y-0=\frac{1}{2}\left( x-4 \right)$ ………………………………………………… (3) For the point $\left( 0,-2 \right)$ , the equation is $y+2=\frac{1}{2}\left( x-0 \right)$ ………………………………………..……. (4) The slope-intercept form can be given by simplifying either equation (3) or (4); we get \begin{align} & y-0=\frac{1}{2}\left( x-4 \right) \\ & y=\frac{1}{2}x-2 \\ \end{align} The slope intercept form of the line is $y=\frac{1}{2}x-2$.