# Graphing a Line using the Slope and [latex]y[/latex]-intercept

To graph a line using its **slope** and [latex]y[/latex]**-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 [latex]y[/latex]-intercept. The slope is just the coefficient of variable [latex]x[/latex] which is [latex]m[/latex], while the [latex]y[/latex]-intercept is the constant term [latex]b[/latex].

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 [latex]y[/latex]-intercept

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

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

The **numerator **tells you how many 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 [latex]y[/latex]-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 [latex]y[/latex]-intercept

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

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

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 [latex]y[/latex]-intercept which is the point [latex]\left( {0, – 2} \right)[/latex].

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

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

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

I know that the slope is [latex]\large{m = {{ – 5} \over 3}}[/latex] and the [latex]y[/latex]-intercept is [latex]b = 3[/latex] or [latex]\left( {0,3} \right)[/latex]. 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 [latex]y[/latex]-intercept of the given equation which is [latex]\left( {0,3} \right)[/latex].

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