## Precalculus (6th Edition) Blitzer

The linear function in slope-intercept form is $y=\frac{x}{4}+\frac{3}{2}$.
Let us consider the coordinates $\left( -2,1 \right)$ and $\left( 6,3 \right)$ as $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ respectively. And find the equation of the function by taking $f\left( x \right)$ as $y$: \begin{align} & \frac{y-{{y}_{1}}}{x-{{x}_{1}}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & \frac{y-1}{x-\left( -2 \right)}=\frac{3-1}{6-\left( -2 \right)} \\ & \frac{y-1}{x+2}=\frac{2}{8} \\ & \frac{y-1}{x+2}=\frac{1}{4} \end{align} Then, simplify it further, to get \begin{align} & 4\left( y-1 \right)=x+2 \\ & 4y-4=x+2 \\ & 4y=x+2+4 \\ & y=\frac{x+6}{4} \end{align} And breaking the terms into individual terms, \begin{align} & y=\frac{x}{4}+\frac{6}{4} \\ & y=\frac{x}{4}+\frac{3}{2} \end{align} Thus, the slope-intercept form is $y=\frac{x}{4}+\frac{3}{2}$.