How do you graph a line using slope?

How to Graph a Line Using Slope

To graph a line using its slope, you need two key pieces of information: the slope ($m$) and a point on the line (often the $y$-intercept).

Definition

The slope of a line measures its steepness and is defined as:

$$ m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} $$

The slope-intercept form of a line is:

$$ y = mx + b $$

where $m$ is the slope and $b$ is the $y$-intercept.

Worked Example

Problem:
Graph the line $y = 2x - 3$ using its slope.

Step 1: Identify the slope and $y$-intercept

• Slope: $m = 2$
• $y$-intercept: $b = -3$

Step 2: Plot the $y$-intercept

• The $y$-intercept is the point $(0, -3)$.
• Plot this point on the $y$-axis.

Step 3: Use the slope to find another point

• Slope $m = 2$ means "rise $2$, run $1$". - From $(0, -3)$, move up $2$ units and right $1$ unit \to $(1, -1)$. - Plot $(1, -1)$. **Step 4: Draw the line** - Draw a straight line through the points $(0, -3)$ and $(1, -1)$. --- ## Takeaways - The slope tells you how \to move from one point \to another: "rise over run." - Start at the $y$-intercept, then use the slope to plot more points.
• Connect the points to graph the line accurately.