We can easily graph any equation given in *slope-intercept* form.

**DEFINITION:** The *slope-intercept* form of a linear equation is given by

\(y = mx + b\)

where \(m\) is the slope of the line, and is the point where the line intercepts the \(y\)-axis (that is, \(b\) is the \(y\)-intercept).

Essentially, when you have a line in slope intercept form, the slope and a point are given to you straight away. You only need to plot the given point, and use the slope to plot another point. Then connect the dots. It’s that easy.

**EXAMPLE:** Sketch the graph of the line whose equation \(y = - {\Large \frac{1}{2}x} + 2\)

**SOLUTION:** Here we have an equation in slope intercept form, with \(m = - \Large \frac{1}{2}\) (that is, the slope of the line is \( - \Large \frac{1}{2}\)), and \(b = 2\) (that is, the \(y\)-intercept is 2). We begin by plotting the \(y\)-intercept:

Next, we use the slope to find our next point. The slope is \( - \Large \frac{1}{2}\), so we move one unit *down* (because of the negative slope) and two units to the right. This puts us at the point \(\left( {2,1} \right)\). Then we connect the dots.

**EXAMPLE:** Sketch the graph of the line whose equation is \(y = - {\Large \frac{7}{5}x} - 5\).

**SOLUTION:** Here we are given another line in slope-intercept form, with \(m = - \Large \frac{7}{5}\), and \(b = - 5\). Then the first point we plot is the \(y\)-intercept at \( - 5\):

Then since the slope is \( - \Large \frac{7}{5}\), we move *down* 7 units, and *right* 5 units. Then connect the dots, and we’re finished!

Below you can** download **some** free** math worksheets and practice.

Sketch the graph of each line.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Sketch the graph of each line.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Sketch the graph of each line.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**