Download Skill Builder 4.1 Graphing Equations in Two Variables

Skill Builder 4.1
Graphing Equations in Two Variables
Complete each table of values for each given equation. Graph the ordered pairs from the table. State
whether the graph represents a linear equation or a quadratic equation.
1.
y=x
x
–2
–1
0
1
2
2.
3.
4.
y = –2x – 1
x
–2
–1
0
1
2
y = –x2 + 1
x
–3
–2
–1
0
1
2
3
y = –2x – 1
(x, y)
(x, y)
y = –x2 + 1
(x, y)
y=2
(x, y)
y = x2 – 1
(x, y)
y=2
x
–2
–1
0
1
2
5.
y=x
y = x2 – 1
x
–3
–2
–1
0
1
2
3
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Skill Builder 4.2
Using Intercepts to Graph
Graphing Using Intercepts
• The value of x is zero at the y-intercept.
• The value of y is zero at the x-intercept.
Complete each table to find the intercepts. Name the intercepts.
x
5x – 3y = 15
y
1. 5x – 3y = 15
(x, y)
0
0
6
x-intercept _________________
y-intercept _________________
2. y = 2x – 4
x
y = 2x – 4
y
(x, y)
0
0
–2
x-intercept _________________
y-intercept _________________
Match each equation with its graph.
3. ______ y = 5
a.
b.
c.
d.
e.
f.
4. ______ x + 3y = –6
5. ______ 4x – 5y = 20
6. ______ x = 5
7. ______ 3x + 7 = –6
8. ______ 2x + 4y = 12
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Skill Builder 4.3
Slope
Choose the correct slope for the line passing through each pair of points.
1. (1, 4) (2, 7)
1
3
b. 1
c.
d. undefined
a. –
3
1
2. (2, 4) (3, 4)
8
a.
5
3. (–3, 5) (2, –8)
5
a. 13
b. 0
b.
c. undefined d.
– 135
c.
11
2
c. 0
13
5
1
8
d. −
13
5
4. (1, 6) (1, 5)
a. undefined b.
2
d. 11
5. Find the slope of each line or state that the line is undefined.
a.
b.
c.
d.
6. Determine if distinct lines through each pair of points are parallel.
a. (3, –4) (2, 8) and (4, 6) (–8, 5)
b. (8, –1) (4, –3) and (–4, 5) (–3, 6)
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Skill Builder 4.4
The Slope-Intercept Form of the Equation of a Line
•
•
The slope-intercept form of a linear equation is y = mx + b.
m is the slope of the line; b is the y-coordinate of the y-intercept.
Fill in the table.
1.
Equation
2
y = x+3
5
2.
3.
y=
y-intercept
m=3
(0, 2)
m=0
(0, –5)
–1
x–3
3
4.
5.
Slope
5x – 6y = 24
Write the equation of the line illustrated in each graph.
6.
9.
7.
8.
10.
11.
Fill in the blanks.
12. A line with a ___________ slope slants up from left to right.
13. A line with a ___________ slope slants down from left to right.
14. A horizontal line has __________ slope.
15. A vertical line has __________ slope.
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Skill Builder 4.5
The Point-Slope Form of the Equation of a Line
Match the information on the left with the correct slope-intercept equation.
1
x+4
2
______ 1.
slope –2 passing through (3,1)
a. y =
______ 2.
passing through (1, 4) (–2, –2)
b. y = 2x
______ 3.
slope 3 passing through (0, 1)
c. y = –x –1
______ 4.
passing through (2, –1) (4, –1)
d. y = x + 4
______ 5.
slope 2 passing through the origin
e. y = 3x + 1
______ 6.
slope –1 passing through (–3, 2)
f. y =
______ 7.
passing through (0, 4) (3, 7)
g. y = –1
______ 8.
slope –3 passing through (1, 0)
h. y = –2x + 7
______ 9.
slope
1
x+5
2
1
passing through (–2, 4)
2
i. y = –4x + 6
______ 10. slope –4 passing through (2, –2)
j. y = –3x + 3
k. x = –1
l. y = 2x + 2
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Skill Builder 4.6
Linear Inequalities in Two Variables
•
•
•
The graph of an inequality in two variables will have a shaded half plane.
A solid boundary line indicates equality.
A dashed (broken) boundary line indicated > or < only.
Match the inequality with its graph.
______1. y < –2
______5. 6x – 3y > –3
______2. 3x – 2y ≥ –4
______6. x + y ≤ 3
______3. x – y < 3
______7. 3x + y ≤ 3
______4. x > –2
______8. 4x + 6y > 6
a.
b.
c.
d.
e.
f.
g.
h.
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