Do you know how to identify the slope in an equation? How about the yintercept?
Take a look at this situation.
\begin{align*}y=2x8\end{align*}
In this Concept, you will learn how to figure out the slope and the yintercept by looking at an equation. We will look at this one again at the end of the Concept.
Guidance
We have seen linear equations in function form, have created tables of values and graphs to represent them, looked at their \begin{align*}x\end{align*}
Remember standard form?
The standard form of an equation is when the equation is written in \begin{align*}Ax+By=C\end{align*}
This form of the equation allows us to find many possible solutions. In essence, we could substitute any number of values for \begin{align*}x\end{align*}
Think back, remember that the slope is the steepness of the line and the \begin{align*}y\end{align*}
We can write an equation in a different form than in standard form. This is when \begin{align*}y = \end{align*}
Slope – Intercept Form is \begin{align*}y=mx+b\end{align*}
Take a look at this graph and equation.
Graph the line \begin{align*}y=3x+1\end{align*}
Here we can calculate the slope of the line using the rise over the run and see that it is 3. The \begin{align*}y\end{align*}
When an equation is in slope – intercept form, we can spot the slope and the \begin{align*}y \end{align*}
\begin{align*}y={\color{red}m}x+ {\color{cyan}b}\end{align*}
Here \begin{align*}m\end{align*}
For any equation written in the form \begin{align*}y=mx+b\end{align*}
Because we can use slope – intercept form, we can rewrite equations in standard form into slope – intercept form. Then we can easily determine the slope and \begin{align*}y\end{align*}
Take a look here.
Write \begin{align*}4x+2y=6\end{align*}
\begin{align*}4x+2y &=6 \\ 4x+2y2y &=62y\\ 4x &=62y\\ 4x6 &=2y\\ \frac{4x6}{2} &=y \\ y &= 2x+3\end{align*}
Now we can determine the slope and the \begin{align*}y\end{align*}
\begin{align*}2 &= \text{slope}\\ 3 &= y  \text{intercept}\end{align*}
Think back to our work with functions. Remember how we could write a function in function form? Well take a look at function form compared with slope – intercept form.
Function form \begin{align*}= f(x)=2x+1\end{align*}
Slope – Intercept Form \begin{align*}= y=2x+1\end{align*}
Yes! The two are the same. These two equations are equivalent!
Determine the slope and the yintercept in each equation.
Example A
\begin{align*}y=x+4\end{align*}
Solution: slope = 1, yintercept = 4
Example B
\begin{align*}2x+y=10\end{align*}
Solution: slope = 2, yintercept = 10
Example C
\begin{align*}3x+y=9\end{align*}
Solution: slope = 3, yintercept = 9
Now let's go back to the dilemma at the beginning of the Concept.
\begin{align*}y=2x8\end{align*}
Looking at this equation, you can see that the slope is \begin{align*}2\end{align*}
Vocabulary
 Slope – Intercept Form

the form of an equation \begin{align*}y=mx+b\end{align*}
y=mx+b
 Standard Form

the form of an equation \begin{align*}Ax+By=C\end{align*}
Ax+By=C
 Slope
 the steepness of the line, calculated by the ratio of rise over run.

\begin{align*}y \end{align*}
y – Intercept 
the point where a line crosses the \begin{align*}y\end{align*}
y axis.
Guided Practice
Here is one for you to try on your own.
Write this equation in slopeintercept form and then determine the slope and the yintercept.
\begin{align*}18x+6y &= 12 \\ 18x+6y &=12 \\ 18x+6y+18x &=18x+12\\ 6y &=18x+12\\ 6y&=18x+12\\ \frac{18x+12}{6} &=y \\ y &= 3x+2\end{align*}
Given this equation, the slope is 3 and the yintercept is 2.
Video Review
Converting to SlopeIntercept Form
Practice
Directions: Look at each equation and identify the slope and the \begin{align*}y \end{align*}

\begin{align*}y=2x+4\end{align*}
y=2x+4 
\begin{align*}y=3x2\end{align*}
y=3x−2  \begin{align*}y=4x+3\end{align*}
 \begin{align*}y=5x1\end{align*}
 \begin{align*}y=\frac{1}{2}x+2\end{align*}
 \begin{align*}y= 2x+4\end{align*}
 \begin{align*}y= 3x1\end{align*}
 \begin{align*}y=\frac{1}{3}x+5\end{align*}
Directions: Use what you have learned to write each in slope – intercept form and then answer each question.
 \begin{align*}2x+4y=12\end{align*}
 Write this equation in slope – intercept form.
 What is the slope?
 What is the \begin{align*}y\end{align*} – intercept?
 \begin{align*}6x+3y=24\end{align*}
 Write this equation in slope – intercept form.
 What is the slope?
 What is the \begin{align*}y\end{align*} – intercept?
 \begin{align*}5x+5y=15\end{align*}
 Write this equation in slope – intercept form.
 What is the slope?
 What is the \begin{align*}y\end{align*} – intercept?