How do I graph a line using slope and intercepts?

Graphing a Line Using Slope and Intercepts

To graph a line using its slope and intercepts, you use the equation of a line in slope-intercept form:

$$ y = mx + b $$

where:

• $m$ is the slope (rise over run)
• $b$ is the $y$-intercept (where the line crosses the $y$-axis)

Steps

1. Plot the $y$-intercept ($b$): This is the point $(0, b)$ on the $y$-axis.
2. Use the slope ($m$): From the $y$-intercept, use the slope to find another point. If $m = \frac{\text{rise}}{\text{run}}$, move up/down (rise) and right/left (run) from the $y$-intercept.
3. Draw the line: Connect the points with a straight line.

---

Worked Example

Graph the line: $y = -2x + 3$

Step 1: Identify the $y$-intercept ($b$):

• $b = 3$
• Plot the point $(0, 3)$

Step 2: Identify the slope ($m$):

• $m = -2 = \frac{-2}{1}$
• From $(0, 3)$, move down $2$ units (since the rise is $-2$) and right $1$ unit (run is $1$) \to get \to $(1, 1)$ **Step 3: Find the $x$-intercept:** Set $y = 0$: %%MATH_DISPLAY_1%% So, the $x$-intercept is $left( frac{3}{2}, 0 right)$ **Step 4: Draw the line:** Connect $(0, 3)$, $(1, 1)$, and $left( frac{3}{2}, 0 right)$ --- ## Takeaways - The $y$-intercept is where the line crosses the $y$-axis; plot this first. - The slope tells you how \to move from one point \to another on the line. - The $x$-intercept can be found by setting $y = 0$ and solving for $x$.