1. Section 2.3 - Quick Graphs of Linear Equations
ALGEBRA TWO
Section Quick Graphs of Linear Equations

2. LEARNING GOALS
Goal One - Use the slope-intercept form of a linear equation to graph linear equations.
Goal Two - Use the standard form of a linear equation to graph linear equations.

3. VOCABULARY
If the graph of an equation intersects the y-axis at the point (0, b), then the number b is the y-intercept.
The slope-intercept form of a linear equation is y = mx + b. 1

4. Graphing Equations in Slope-Intercept Form
The slope-intercept form of an equation gives you a quick way to graph the equation.
STEP 1: Write the equation in slope-intercept form by solving for y.
STEP 2: Find the y-intercept and use it to plot the point where the line crosses the y-axis.
STEP 3: Find the slope and use it to plot a second point on the line.
STEP 4: Draw a line through the two points. 1

5. Graphing Equations in Slope-Intercept Form
PROBLEM: Graph 2x + y = 3
SOLUTION
STEP 1: Write equation in slope-intercept form.
2x + y = 3
Write original equation
y = -2x + 3
Subtract 2x from each side
STEP 2: The y-intercept is 3, so plot the point (0, 3).

6. Graphing Equations in Slope-Intercept Form
PROBLEM: Graph 2x + y = 3
SOLUTION
STEP 3: The slope is -2/1, so plot a second point by moving 1 unit to the left and 2 units up. This point is (-1, 5).

7. Graphing Equations in Slope-Intercept Form
PROBLEM: Graph 2x + y = 3
SOLUTION
STEP 4: Draw a line through the two points.

8. VOCABULARY The standard-form of a linear equation is
Ax + By = C, where A and B are not both zero.
The y-intercept is the y-coordinate of the point where the graph crosses the y-axis and is found by letting x = 0 and solving for y.
The x-intercept is the x-coordinate of the point where the graph crosses the x-axis and is found by letting y = 0 and solving for x. 1

9. Graphing Equations in Standard Form
The standard form of an equation gives you a quick way to graph the equation.
STEP 1: Write the equation in standard form.
STEP 2: Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis.
STEP 3: Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis.
STEP 4: Draw a line through the two points. 1

10. PROBLEM: Graph -2x +3y = -6 Graphing with the Standard Form
SOLUTION
STEP 1: The equation is in standard form.
-2x + 3y = -6
STEP 2: Find the x-intercept.
-2x + 3(0) = -6
Substitute 0 for y.
-2x/-2 = -6/-2
Divide each side by -2
x = 3
Simplify
The x-intercept is (3, 0) 1

11. Graphing with the Standard Form STEP 3: Find the y-intercept.
PROBLEM: Graph -2x +3y = -6
SOLUTION
STEP 3: Find the y-intercept.
-2(0) + 3y = -6
Substitute 0 for x.
3y/3 = -6/3
Divide each side by 3
y = -2
Simplify
The y-intercept is (0, -2) 1

12. PROBLEM: Graph -2x +3y = -6 Graphing with the Standard Form
SOLUTION
STEP 4: Draw a line through the two points (3, 0) and (0, -2). 1

13. Using the Standard Form
PROBLEM: Sales for the firefighters benefit dinner were $ The cost for a child’s dinner was $4.50 and an adult’s dinner was $ Describe the number of children and adults who attended to reach this amount.
SOLUTION
WRITE A VERBAL MODEL.
TIMES
Cost per child
Number of children
PLUS
Cost per adult
TIMES
Number of adults
EQUALS
Total Revenue

14. Using the Standard Form WRITE AN ALGEBRAIC MODEL.
PROBLEM: Sales for the firefighters benefit dinner were $ The cost for a child’s dinner was $4.50 and an adult’s dinner was $ Describe the number of children and adults who attended to reach this amount.
SOLUTION
WRITE AN ALGEBRAIC MODEL.
4.50c a = 1980
The graph of this equation is a line that intersects the c-axis at (440, 0) and the a-axis at (0, 330). Points along this line represent the number of combinations of people that could have attended.

15. Review slope-intercept form of a linear equation is y = mx + b.
STEP 1: Write the equation in slope-intercept form by solving for y.
STEP 2: Find the y-intercept and use it to plot the point where the line crosses the y-axis.
STEP 3: Find the slope and use it to plot a second point on the line.
STEP 4: Draw a line through the two points.
standard-form of a linear equation is
Ax + By = C, where A and B are not both zero.
STEP 1: Write the equation in standard form.
STEP 2: Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis.
STEP 3: Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis.
STEP 4: Draw a line through the two points.

16. Homework
pg #
21, 23, 25, 29, 31, 35, 41, 45, 49, 57