__Graphing Linear Equations__Chapter 3

**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 - y _{1}= m(x - x_{1})(x is a particular point on the line.m is the slope of the line._{1}, y_{1})

(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:

- Set y = 0 in the equation.
- Solve for x. The value obtained is the x-coordinate of the x-intercept.
- 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:

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

**Graphing Lines by Plotting Points**- The idea:
- Find two points on the line.
- Plot the two points.
- Draw a straight line between the two points.

- Finding two points on the line:
- Pick a value for x (or y).
- Solve for y (or x, if you picked a value for y).
- The point
(x, y) is a point on the line. - 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 formx = a are vertical lines.

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

**Horizontal Lines**

Equations of the formy = a are horizontal lines.

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