Download Linear Equations and Functions

HSA Practice Problem Set #1:
Linear Equations and Functions
1. What is the slope of the line passing through the
points  6,  5 and  2, 11 ?
4
3
2
[D]
3
3
4
1
[E]
4
[A]
[B]
[C]
5. What is the equation of the line whose graph is
shown below?
1
2
2. What is the slope of the line whose graph is
shown below?
[A] y 1  34  x  4
[B] y  7  34  x  4
[C] y  7  43  x  4
[D] y 1  43  x  4
[E] y  7   34  x  4
[A] 
[D]
3
4
3
4
4
3
1
[E] 
2
[B] 
[C]
4
3
6. Which of the following is an equation for the
line passing through the  4, 9  and  2, 6  ?
[A] 2 x  y  10  0
[B] 2 x  3 y  14  0
[C] x  2 y  14  0
[D] x  2 y  10  0
[E] x  2 y  10  0
3. The line passing through the points  5,  4
5
and  3, r  has a slope of  . What is the
4
value of r ?
12
3
[A]
[B] 
[C] 14
5
2
[D] 6
[E] 9
7. What is the slope of the line with equation
6 x  10 y  8 ?
5
5
4
[A]
[B] 
[C]
3
3
5
3
3
[D] 
[E]
4
5
4. A line passes through the point  4,  3 and
has slope 0 . Which of the following is another
point on the line?
[A]  4, 1
[B]  4,  7 
[C]  2, 3
[D]  5,  3
[E]  4, 3
8. Which equation has a slope of 3 ?
[A] x  3 y  12
[B] 3x  y  11
[C] 6 x  2 y  7
[D] 9 x  3 y  0
[E] x  3 y  15
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HSA Practice Problem Set #1:
Linear Equations and Functions
9. Which of the following shows the graph of y  32 x  4 ?
[A]
[B]
[D]
[E]
10. Which of the following shows the graph of 4 x  2 y  5 ?
[A]
[B]
[D]
[C]
[E]
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[C]
HSA Practice Problem Set #1:
Linear Equations and Functions
11. The line y  3 x  5 is translated 6 units up.
What is the equation of the resulting image?
[A] y  3x  6
[B] y  9 x  5
[C] y  3x  11
[D] y  3x  5
[E] y  3x  1
14. Which table of values represents a linear
function?
[A]
y
–3
1/ 3
–1
–1
1
1
3
1/ 3
x
y
0
–3
1
–1
2
1
4
5
x
–2
3
–1
1
1
–1
2
–3
y
–6
4
–4
3
0
0
8
–3
x
y
2
1
2
3
2
5
2
7
x
[B]
[C]
y
[D]
x
[E]
12. The line graphed above is rotated 90° about it’s
y-intercept. What is the equation of the
resulting image?
5
[A] y   x  6
6
6
[B] y  x  6
5
5
[C] y  x  5
6
6
[D] y   x  5
5
5
[E] y   x  5
6
x
y
–4
–3
–1
a
15. Let f be a linear function with slope 4 / 3 and
y-intercept 1 . What is f  6  ?
[A] –7
[B] –9
[C] 7
5
9
[D]
[E] 
2
2
1
7
13. The table above shows values of a linear
relation. What is the value of a?
[A] 1/ 2
[B] 1
[C] 1
[D] 3 / 2
[E] 3
16. The graph of a linear function f is shown
above. What is f  30 ?
[A] 122
[D] 7.5
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[B] 32
[E] 9.5
[C] 5.5
HSA Practice Problem Set #1:
Linear Equations and Functions
17. Which graph shows the image of x  3 y  12 after it is translated 1 unit down?
[A]
[B]
[C]
[D]
[E]
18. Which of the following shows the graph of x  1  3  x  5 ?
[A]
[B]
[D]
[E]
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[C]
HSA Practice Problem Set #1:
Linear Equations and Functions
19. The slope of the line passing through the points  4,  6  and  4,  2 is
.
20. The slope of the line passing through the points  3, 5 and  3,  1 is
.
21. The slope of the line passing through the points 13, 21 and  11,  24 is
.
22. The slope of the line passing through 1,  9  and  11, v  is 5 / 4 . Therefore, v 
.
23. The slope of the line passing through  5,  6 and  u,  1 is 2 / 3 . Therefore, u 
.
For problems 24 through 27, graph the line satisfying the following conditions on the axes provided.
24. y-intercept 4, slope –5
25. passes through  7,  2 , slope 2 / 5
27. passes through  3.5, 1.25 , slope 0
26. x-intercept –4, undefined slope
28. The line with y-intercept 7 and slope 3 has equation
y =
x +
29. The line passing through  6, 0  with slope 3 / 4 has equation y 
x+
30. The line passing through  9, 12 and  3, 4  has equation
31. The equation y  6  0 has slope
and y-intercept
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.
x+
.
.
y=
.
HSA Practice Problem Set #1:
Linear Equations and Functions
For problems 32 through 35, graph the line with the given equation.
32. y  73 x  6
33. x  9 y  18  0
34. y  3  4  x  5
35. 4x 10  0
36. The line 4 x  6 y  3  0 is translated 2.5 units down. The equation of the resulting image is
y
.
x+
37. The equation of the line passing through  6, 8 perpendicular to the line y  3x  2 is
x+
y=
.
38. The graph of a line and a point P is shown below. The equation of the line passing through P and the line
graphed is y 
.
x+
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HSA Practice Problem Set #1:
Linear Equations and Functions
For problems 39 and 40, each table below shows values for a linear function. Complete the table by
filling in the values for the empty cells.
39.
x
–3
–1
y
7
1
x
0
1
0
1
3
3
6
10
40.
y
–8
–2
41. If f  x   8x  13 , then f  4 
.
42. Let g be the linear function with slope 
2
 1
and y-intercept 4 . g    
5
 4
.
For problems 43 and 44, let f and g be the functions shown in the graphs.
43. f  9 
44. f 1/ 4  
45. The point  h,  4  lies on the line y 
2
 x  3 . Therefore, h 
3
46. The point  6, k  lies on the line 3x  8 y  2 . Therefore, k 
47. The points  3, 1 ,  9, 5 , and  0, b  lie on a line. Therefore, b 
48. The graph of y 
5
x  15 has x-intercept
8
.
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.
.
.