Holt CA Course 1
2-8 Graphing Equations
AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.Also covered: NS2.3
California Standards
Holt CA Course 1
2-8 Graphing Equations
Vocabulary
linear equation
An equation whose solutions form a straight line on a coordinate plane.
Holt CA Course 1
2-8 Graphing EquationsExample 1: Finding Solutions of Equations with
Two Variables
Use the given x-values to write solutions of the equation as ordered pairs. y = 4x + 2; x = 1, 2, 3, 4.Make a table by using the given values for x to find values for y.
x 4x + 2 y
1 4(1) + 2 6
2 4(2) + 2 10
3 4(3) + 2 14
4 4(4) + 2 18
Write these solutions as ordered pairs.
(x, y)
(1, 6)
(2, 10)
(3, 14)
(4, 18)
Holt CA Course 1
2-8 Graphing Equations
Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.
Holt CA Course 1
2-8 Graphing Equations
Example 2: Checking Solutions of Equations with Two Variables
Determine whether the ordered pair is a solution to the given equation.
(3, 21); y = 7x
y = 7x Write the equation.
21 = 7(3)?
21 = 21?
Substitute 3 for x and 21 for y.
So (3, 21) is a solution to y = 7x.
Holt CA Course 1
2-8 Graphing Equations
You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs given by some equations, they form a straight line. For this reason, these equations are called linear equations.
Holt CA Course 1
2-8 Graphing EquationsExample 3: Reading Solutions on Graphs
Use the graph of the linear equation to find the value of y for the given value of x.
x = 4
When x = 4, y = 2.
Start at the origin and move 4 units right.
Move up until you reach the graph. Move left to find the y-value on the y-axis.
The ordered pair is (4, 2).
x
y
-4 -2 0 2 4
4
-2
-4
2
Holt CA Course 1
2-8 Graphing Equations
Example 4: Graphing Linear Functions
Graph the equation y = –x – 2.
Make a table. Substitute different values for x.
x –x – 2 y
–1 –(–1) – 2 –1
0 –(0) – 2 –2
1 –(1) – 2 –3
Write the solutions as ordered pairs.
(x, y)
(–1, –1)
(0, –2)
(1, –3)
Holt CA Course 1
2-8 Graphing Equations
Example 4 Continued
x
y
Graph the ordered pairs on a coordinate plane.
-5 -4 -3 -2 -1 0 1 2 3 4 5
543
2
1
-5
-4-3-2
-1
Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.
Holt CA Course 1
2-8 Graphing Equations Check It Out! Example 1
Use the given x-values to write solutions of the equation as ordered pairs. y = 3x + 2; x = 2, 3, 4, 5.
Make a function table by using the given values for x to find values for y.
x 3x + 2 y
2 3(2) + 2 8
3 3(3) + 2 11
4 3(4) + 2 14
5 3(5) + 2 17
Write these solutions as ordered pairs.
(x, y)
(2, 8)
(3, 11)
(4, 14)
(5, 17)
Holt CA Course 1
2-8 Graphing EquationsCheck It Out! Example 2
Determine whether the ordered pair is a solution to the given equation.
(4, 20); y = 5x
y = 5x Write the equation.
20 = 5(4)?
20 = 20?
Substitute 4 for x and 20 for y.
So, yes (4, 20) is a solution to y = 5x.
Holt CA Course 1
2-8 Graphing Equations Check It Out! Example 3
Use the graph of the linear function to find the value of y for the given value of x.
x = 2
When x = 2, y = 4.
Start at the origin and move 2 units right.
Move up until you reach the graph. Move left to find the y-value on the y-axis.
The ordered pair is (2, 4).
x
y
-4 -2 0 2 4
4
-2
-4
2
Holt CA Course 1
2-8 Graphing Equations
Check It Out! Example 4
Graph the equation. y = –x – 4
Make a table. Substitute different values for x.
x –x – 4 y
–1 –(–1) – 4 –3
0 –(0) – 4 –4
1 –(1) – 4 –5
Write the solutions as ordered pairs.
(x, y)
(–1, –3)
(0, –4)
(1, –5)
Holt CA Course 1
2-8 Graphing Equations
Check It Out! Example 4 Continued
x
y
Graph the ordered pairs on a coordinate plane.
-5 -4 -3 -2 -1 0 1 2 3 4 5
543
2
1
-5
-4-3-2
-1
Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.
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