Ordered Pairs, Intercepts, And Slopes Worksheet Page 4
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18Chapter — Graphng
0
t
echniQues
1
Find Ordered Pair Solutions to a Linear Equation
1. Choose any value for x (or y).
2. Solve for y (or x).
3. Validate by substituting the ordered pair back into the equation.
►
Example 1: Find an ordered pair solution for the equation 2x + 3y = 10
Choose a value for x: Let x = –4
or y: Let y = –2
2 +3 =10
x
y
2 +3 =10
x
y
2(–4)+3 =10
y
2 +3(–2)=10
x
–8+3 =10
y
2 – 6 =10
x
+8 – 8+3 =10+8
y
2 – 6+6 =10+6
x
3 =18
y
2 =16
x
3
y
18
2
x
16
=
=
3
3
2
2
y
= 6
x
= 8
An ordered pair solution is: (8, –2)
An ordered pair solution is: (–4, 6)
?
?
= 10
Validate:
2(8) + 3(–2)
Validate:
2(–4) + 3(6)
= 10
?
?
16 – 6
= 10
–8 + 18
= 10
10 = 10
10 = 10
2
Find the x- and y-Intercepts for a Linear Equation
1. To find an x-intercept, let y = 0 and solve for x.
2. To find a y-intercept, let x = 0 and solve for y.
3. Validate by substitution.
►
Example 2: Find the x and y-intercepts for the equation 2x + 3y = 10
x-intercept: let y = 0 and solve for x:
y-intercept: let x = 0 and solve for y:
2(0)+3 =10
y
2 +3(0)=10
x
3 =10
y
2 =10
x
3
y
10
2
x
10
=
=
3
3
2
2
10
10
x
=5
The x - intercept is (5, 0).
y
=
The y - intercept is (0,
).
3
3
?
= 10
Validate:
2(5) + 3(0)
10
?
Validate:
2(0) + 3(
)
= 10
3
10 = 10
10 = 10
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