1. 4.2 Graphing Linear Equations

2. Solution of a Linear Equation
Is an ordered pair (x, y) that makes the equation true.
Example: Determine whether the ordered pair is a solution of x + 2y = 5.
a) (1, 2) b) (7, -3)

3. Writing Linear Equations in Slope-Intercept Form
An equation is in slope intercept form when “y” is isolated (it is by itself on one side of the equal sign).
y = mx + b

4. Example 2: Write the equation in slope – intercept form
-2x + y = -3

5. You Try It…
Write each equation in slope-intercept form. Then identify the slope and the y-intercept.
-3x + y = 12
2) 4y – 2x = 8
3) 5x + 2y + 15 = 0
4) -5x – 3y = 12

6. Graphs of Linear Equations
The graph of an equation in x and y is the set of ALL points (x, y) that are solutions to the equation.
The graph of a linear equation can be shown to be a straight line.

7. We can use Slope-Intercept form to Graph Equations
Steps:
1) Write the equation in slope-intercept form (get “y” alone).
2) Identify slope (m) and y-intercept (b).
3) Plot the y-intercept.
4) Use the slope (rise/run) to plot at least 2 more points).
5) Connect all points with a straight line (USE A RULER!).

8. Example 3 Find the slope and y-intercept of y = -3x + 2
Then graph the equation.

9. Example 4 Find the slope and y-intercept of 2x – y = -3
Then graph the equation.

10. You Try It… Find the slope and y-intercept of each equation.
Then graph the equation.
y = -2x
y = 4x – 5
y = x + 2

11. Application
Andrew has a small business making decorated hats. Based on data for the last eight months, he calculates his monthly cost y of producing x hats using the equation y = 1.9x
A) Explain what the y-intercept and the slope mean in this model.
B) graph the model. Then use the graph to estimate the cost of 35 hats.