Graphs of Lines

Graphing Linear Equations - Slope y-Intercept Form

1. If the equation is not already in slope y-intercept form, rewrite it into this form $\boxed{y=mx+b}$
2. If the slope isn't already in fraction form, rewrite it as a fraction $\boxed{m=\dfrac{\text{rise}}{\text{run}}}$
3. Plot the $\boxed{y\text{-intercept}}$ *You can also just plot any point $(x_1,y_1)$ that's on the line
4. From this point, use the slope to determine another point on the graph
5. If $m$ is positive, go up "rise" units, and go to the right "run" units
6. If $m$ is negative, go down "rise" units, and go to the right "run" units
7. Connect these two points and you have a line!

1. Rewriting this: $y=-2x+3$
2. The slope is $m=\dfrac{-2}{1}$
3. The y-intercept is 3.
4. Starting at $(0,3)$, go down 2 and right 1

1. We arrive at the point $(1,1)$. Connect this point with the y-intercept and we have our line!

Graphing Linear Equations - Using Intercepts

Recall

• The $\bcf x$-intercept is where the graph of the line crosses the $x$-axis (horizontal axis)
• The $\bcf y$-intercept is where the graph of the line crosses the $y$-axis (vertical axis)

1. Find the $\bcfi{x\text{-intercept}}$ by setting $\bcfi{y=0}$ then solving for the $x$ value
2. Find the $\bcfi{y\text{-intercept}}$ by setting $\bcfi{x=0}$ then solving for the $y$ value
3. Plot these two intercept points on the graph
4. Connect these two points to get the graph of your line!

1. Set $y=0$: $\begin{array}{rcl} 2x+\colorFour 0-3&=&0\\ 2x-3&=&0\\ 2x&=&3\\ \dfrac{2x}{2}&=&\dfrac{3}{2}\\ x&=&\dfrac{3}{2} \end{array}$ So the $x$-intercept is $\dfrac{3}{2}$ (meaning the line crosses the $x$-axis at $x=\dfrac{3}{2}$)
2. Set $x=0$: $\begin{array}{rcl} 2(\colorFour 0)+y-3&=&0\\ y-3&=&0\\ y&=&3 \end{array}$ So the $y$-intercept is $3$ (meaning the line crosses the $y$-axis at $y=3$)
3. Plot the two intercepts:
4. Connecting these points we get our linear graph!