# Graphing a Line using the Slope and y-intercept

To graph a line using its **slope** and y**-intercept**, we need to make sure that the equation of the line is in the Slope-Intercept Form,

From this format, we can easily read off both the values of the slope and y-intercept. The slope is just the coefficient of variable x which is m, while the y-intercept is the constant term b.

Here’s a quick diagram to emphasize this idea.

When these two pieces of information are identified, we are guaranteed to successfully graph the equation of the line.

## How to Graph a Line using the Slope and y-intercept

- Plot the y-intercept \left( {0,b} \right) in the xy axis. Remember, this point always lies on the vertical axis y.

- Starting from the y-intercept, find another point using the slope. Slope contains the direction how you go from one point to another.

The **numerator **tells you how much steps to go **up or down** (rise) while the **denominator** tells you how many units to move **left or right** (run).

- Connect the two points generated by the y-intercept and the slope using a straight edge (ruler) to reveal the graph of the line.

### Examples of Graphing a Line using the Slope and y-intercept

**Example 1:** Graph the line below using its slope and y-intercept.

Compare y = mx + b to the given equation y = {3 \over 4}x - 2. Clearly, we can identify both the slope and y-intercept. The y-intercept is simply b = - 2 or \left( {0,2} \right) while the slope is m = {3 \over 4}.

Since the slope is positive, we expect the line to be increasing when viewed from left to right.

**Step 1:**Let’s plot the first point using the information given to us by the y-intercept which is the point \left( {0, - 2} \right).

**Step 2:**From the y-intercept, find another point using the slope. The slope is m = {3 \over 4}, that means, we go up 3 units and move to the right 4 units.

**Step 3:**Connect the two points to graph the line.

**Example 2:** Graph the line below using its slope and y-intercept.

I know that the slope is m = {{ - 5} \over 3} and the y-intercept is b = 3 or \left( {0,3} \right). Since the slope is negative, the final graph of the line should be decreasing when viewed from left to right.

**Step 1:**Begin by plotting the y-intercept of the given equation which is \left( {0,3} \right).

**Step 2:**Use the slope m = {{ - 5} \over 3} to find another point using the y-intercept as the reference. The slope tells us to go down 5 units and then move 3 units going to the right.

**Step 3:**Draw a line passing through the points.

**You might also be interested in:**

Three Ways to Graph a Line

Graphing a Line using Table of Values

Graphing a Line Using X and Y intercepts