How to Draw a Line Segment with a Slope

Drawing a line segment with a specific slope involves identifying a starting point and using the slope value to locate a second point. Connecting these two points creates the segment.

Understanding Slope

The slope of a line or line segment tells us how steep it is. It's defined by the ratio of vertical change to horizontal change between any two points on the line.

The formula for slope is:
$m = \frac{\text{rise}}{\text{run}}$

Here:

• Rise is the vertical change (movement up or down).
• Run is the horizontal change (movement left or right).

A positive slope means the line goes up from left to right, while a negative slope means it goes down from left to right.

Steps to Draw a Line Segment Using Slope

To draw a line segment when you know its slope and at least one point it passes through, follow these steps:

1. Plot the First Point: Start by plotting a known point on your graph. If you are only given a slope (e.g., $m = \frac{3}{4}$) and not a point, you can choose any point to begin with (like the origin, (0,0)), although typically you'd be given at least one point or an equation.

2. Use the Slope to Find the Second Point: Utilize the slope formula $m=\frac{\text{rise}}{\text{run}}$ to identify the rise and the run.

   • From the point you just plotted, count out the rise (vertical movement).
     • A positive rise means count up.
     • A negative rise means count down.
   • From that temporary vertical position, count out the run (horizontal movement).
     • A positive run means count right.
     • A negative run means count left.
   • Mark this location. This is your second point.

   Example: If your slope is $m = \frac{3}{4}$, the rise is 3 and the run is 4. Starting at your first plotted point, you would count 3 units up and then 4 units right to find your second point.

3. Connect the Points: Draw a straight line segment that connects your first plotted point to your second marked point. Unlike a full line, a line segment has clear start and end points, so you do not draw arrows at the ends.

By following these steps, you use the slope to determine the direction and steepness from a starting point to find another point, enabling you to draw the specific line segment.