Algebra 2
Review 3.4-3.7
Linear Equations
Name:
Date:
Period:
Section 3.4
Determine if the following equations are linear. If not, explain why not.
5
1
1. y  x  7
2.
x  9 y  24
3
2
4. x  12
5. 25  5xy
Graph each equation using x- and y- intercepts.
7. 7 x  3 y  21
9. x  6
2
x4
y  3x 2  5
y
3.
6.
8. 5x  2 y  10
10.
y  2  3
Write each equation in standard form using integers (no fractions or decimals allowed).
2
11. y  4 x  11
12.
y  x  25
3
1
5
2
13.
14. y  3   x  10 
x  2y  
4
6
5
Sections 3.5-3.6
Find the slope of each line.
y
15.
5
–5
–4
–3
–2
y
16.
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
y
17.
–4
–3
–2
4
3
3
2
2
1
1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
Find the slope of the line that passes through each pair of points.
19. 1,2 and  4,3
20.  4,5 and
21.
 4, 2
and
3
4
5
x
1
2
3
4
5
x
5
4
–1
–1
2
y
18.
5
–5
1
 4,9
22.
 3, 2
and
3, 4
 4, 2
Find the value of r, given the slope of the line through each pair of points.
4
23. m   ;  r ,1 and  2, r 
3
Graph each equation using slope and y-intercept.
2
24.
y   x6
3
25.
Write an equation of a line with the given slope and point.
1
26. m 
27.
and  0, 3
4
28. m  0 and  2,1
29.
Write an equation of a line with the given points.
30.  0,3 and  3,0
5,3
33.
Write the equation of the line shown below.
34.
y
35.
32.
 2,3
31.
–5
–4
–3
and
–2
2 y  8  6x
2
and  6,4
3
no slope and  2,1
m
 1,2
 4,2
and
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
 1,5
 2,5
and
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
36. A jeweler’s salary was $28,500 in 2000 and $32,900 in 2004. The jeweler’s salary follows a linear growth
pattern. Write an equation to model this growth (assume year 2000 is t=0). What will the jeweler’s salary be in
2005?
Section 3.7
Determine if each line is parallel, perpendicular, or neither.
1
y  x6
37.
38.
2
y  2 x  6
39.
x9
y  2
40.
5
x
2
y  2 x
y
2 x  3 y  18
4 x  6 y  24
Solve the problem.
41. Prove the triangle with vertices (3,5), (-2,6) and (1,3) is a right triangle.
Algebra 2
Review 3.4-3.7
Write an equation of a line that is…
3
42. parallel to y   x  5 and passes through the point  6,7 
2
3
43. perpendicular to y   x  5 and passes through the point 9, 12
2
44.
vertical and passes through the point  5,10
45.
horizontal and passes through the point  5,10
46.
with an x-intercept of 4 and y-intercept of 3
Linear Equations
ANSWER KEY
1.
yes
2.
yes
3.
no, you can’t have a variable in the denominator, when you cross multiply you will get a product of variables
4.
yes
5.
no, you can’t have a product of variables
6.
no, it is second degree ~ no exponent other than 1 for the variables
Your graphs should include the following points for #7-10.
7.
3,0
9.
vertical
11.
and
0,7
8.
6,0
 2,0
and
0, 5
10.
horizontal
4 x  y  11
12.
2 x  3 y  75
13.
3x  24 y  10
14.
2 x  5 y  35
15.
m
1
4
16.
m
17.
m0
18.
no slope
19.
m
1
3
20.
m
22.
m0
21.
and
no slope
and
0, 5
1
3
9
7
23. r  11
Your graphs should include the following points for #24-25.
24.
0,6
25.
0, 4
26.
y
27.
y
28.
y 1
29.
x  2
30.
y  x 3
31.
x  1
32.
y3
33.
y
and
3,4
1
x 3
4
34.
2
x 8
3
3
x 8
2
35.
36.
; $34,000
37.
perpendicular
38.
neither
39.
perpendicular
40.
parallel
41.
Two of the slopes are opposite reciprocals; m = 1 and m = -1
and
1, 1
Algebra 2
Review 3.4-3.7
3
42.
y   x2
2
44.
x  5
46.
3
y  x3
4
Linear Equations
2
x  18
3
43.
y
45.
y  10