Math 101 Intermediate Algebra

Graphing Linear Equations
Chapter 3, Section 2

General Concepts About Linear Equations

A linear equation is the equation of a line.

The graph of a line is a graphical view of the set of all points that make the equation true (in other words, all points that work in the equation or all points that satisfy the equation).

Forms of Equations of Lines

a, b, c, and m are real numbers

Form Equation Note
Standard ax + by = c a and b are not both 0.
Slope-Intercept y = mx + b m is the slope of the line.

(0, b) is the y-intercept.

(discussed in Section 3.3)

Point-Slope y - y1 = m(x - x1) (x1, y1) is a particular point on the line.

m is the slope of the line.

(discussed in Section 3.3)

x-intercept

The x-intercept is the point where the graph crosses the x-axis.

The y-coordinate of the x-intercept is 0.

To find the x-intercept:

1. Set y = 0 in the equation.
2. Solve for x. The value obtained is the x-coordinate of the x-intercept.
3. The x-intercept is the point (x, 0), with x the value found in step 2.

y-intercept

The y-intercept is the point where the graph crosses the y-axis.

The x-coordinate of the y-intercept is 0.

To find the y-intercept:

1. Set x = 0 in the equation.
2. Solve for y. The value obtained is the y-coordinate of the y-intercept.
3. The y-intercept is the point (0, y), with y the value found in step 2.

Graphing Lines by Plotting Points

The idea:
1. Find two points on the line.
2. Plot the two points.
3. Draw a straight line between the two points.

Finding two points on the line:
1. Pick a value for x (or y).
2. Solve for y (or x, if you picked a value for y).
3. The point (x, y) is a point on the line.
4. Repeat steps 1 - 3 for a different value of x (or y).

An easy choice is to find the x-intercept (by setting y = 0 and solving for x).

Another easy choice is to find the y-intercept (by setting x = 0 and solving for y).

Vertical Lines

Equations of the form x = a are vertical lines.

The x-coordinate of every point on the vertical line x = a has the value "a".

Horizontal Lines

Equations of the form y = a are horizontal lines.

The y-coordinate of every point on the horizontal line y = a has the value "a".