## Precalculus (6th Edition) Blitzer

For a $y$ -intercept $b$ of a line, use point-slope form of the line’s equation with $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 0,b \right)$ and solve it for $y$.
Consider a line with slope $m$ and $y$-intercept $b$. Follow the steps given below to find the slope-intercept form of the line from point-slope form: Step 1: Write the slope-intercept form of the line as given below: $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ Step 2: Since the $y$-intercept of the line is $b$, the line will pass through the point $\left( 0,b \right)$. Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 0,b \right)$. \begin{align} & y-{{y}_{1}}=m\left( x-{{x}_{1}} \right) \\ & y-b=m\left( x-0 \right) \end{align} Step 3: Simplify the equation. \begin{align} & y-b=m\left( x-0 \right) \\ & y-b=mx \end{align} Step 4: Calculate $y$. \begin{align} & y-b=mx \\ & y=mx+b \end{align} So, the slope-intercept form of the equation of a line is given by $y=mx+b$. Example: Consider a line with slope $m=2$ and y-intercept 3. The slope-intercept form of line is given below: $y=mx+b$ Replace $m=2\text{ and }b=3$, The equation of the line thus obtained is as follows: $y=2x+3$