# Graphing Linear Equations by Finding Intercepts

Steps for Graphing with the Intercept Method

1. Find the x intercept and the y-intercept.
• To find an x-intercept let y=0 and solve for x.
• To find a y-intercept let x=0 and solve for y.
2. Plot the x-intercept and y-intercept.
3. Draw the line that connects the intercepts.

Example:   Graph the linear equation

Solution:

1. Find the x-intercept and the y-intercept.

To find an x-intercept: Let y=0 and solve for x.

The x-intercept of this equation is

To find a y-intercept: Let x=0 and solve for y.

The y-intercept of this equation is

2. Plot the x-intercept and the y-intercept.

3. Draw the line that connects the intercepts.

Example:   Graph the linear equation

Solution:

1. Find the x-intercept and the y-intercept.

To find an x-intercept: Let y=0 and solve for x.

The x-intercept of this equation is

To find a y-intercept: Let x=0 and solve for y.

The y-intercept of this equation is

Since the x-intercept and the y-intercept are the same point and we need two distinct points to graph a line, we must find another ordered pair that is a solution to the equation.

Let x=1 and find the associated y value. (I chose x=1 but you could choose a different value)

Another ordered pair on the graph is

2. Plot the x-intercept and the y-intercept.

3. Draw the line that connects the intercepts.

Example: Graphing a linear equation with intercepts.

Example: Graphing a linear equation with intercepts.

Example: Graphing a linear equation with intercepts.

# Calculating Slope

Given two points on the line and , you can calculate the slope of a line by the following formula.

is also know as  or “the change in y.”

is also know as  or “the change in x.”

Example: Calculate the slope of the line containing the points and .

Solution: Choose one of the points to be and choose the other point to be .

I will choose   to be   and choose to be .

Substitute these values into the slope formula and simplify.

The slope of the line containing the points and   is .

Example: Calculate the slope of the line containing the points and .

Solution: Choose one of the points to be and choose the other point to be .

I will choose   to be   and choose to be .

Substitute these values into the slope formula and simplify.

The slope of the line containing the points and   is .

Example: Finding the slope with the formula.

Example: Finding the slope with the formula.

Example: Finding the slope from the graph.

# Interpretation of slope

The slope of a line is a number that indicates the “steepness” of a line.  Slope is usually denoted with the letter m.

If the slope of the line is positive, the line will be rising or increasing from left to right.

All three of the above graphs have a positive slope and the line is rising or increasing from left to right.  Notice as the value of the slope gets larger, the line is getting steeper.

If the slope of the line is negative, the line will be falling or decreasing from left to right.

All three of the above graphs have a negative slope and the line is falling or decreasing from left to right.  Notice as the value of the slope gets smaller, the line is getting steeper.

If the slope is zero, the line will be constant.  This results in a horizontal line.

All three of the the above graphs have a slope of zero.  The y values are constant.

A vertical line has a slope that is undefined.

All three of the vertical lines have undefined slope.