Answer
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 $y$.
Work Step by Step
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:
$y=2x+3$
