Linear Equations Reveiw
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SUMMARY OF ALGEBRA CONCEPTS – EQUATIONS & FORMULAS
y  mx  b
Slope Intercept Form
STRENGTHS:
(Graphing, Finding slope, Finding y intercept)
(m is the slope and b is the y-Intercept)
y  y1  m( x  x1 )
Point Slope Form
STRENGTHS:
(Easy to create equation)
(m is the slope and ( x1 , y1 ) is a point)
Ax  By  C
Standard Form
STRENGTHS:
(Find x & y intercepts, System of Equations)
(The A coefficient must be positive and
No Fractions for any values of A, B and C.)
SYSTEM OF EQUATION
Method #1 – Graphing
2x + y = 5
y = -4x + 7
Method #2 – Substitution
2x + y = 5
y = -4x + 7
2x + (-4x + 7) = 5
-2x + 7 = 5
-2x =--2
x=1
6
4
2
y = -4(1) + 7 = 3
Method #3 - Elimination
2x + y = 5
y = -4x + 7
2x + 1y = 5
4x + 1y = 7 (subtract)
-2x + 0y = -2
x=1
y = -4(1) + 7 = 3
5
Answer (1,3)
Answer (1,3)
Answer (1,3)
KEY FORMULAS
DISTANCE FORMULA
 x2  x1    y2  y1 
2
SLOPE FORMULA
y2  y1
m
x2  x1
MIDPOINT FORMULA
2
x1  x2 y1  y2 
,

2 
 2
 xm , ym   
PYTHAGOREAN THEOREM
a 2  b2  c2
QUADRATIC EQUATION
2
0  ax  bx  c
b  b2  4ac
x
2a
Linear Equations Reveiw
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1. Given points A (-2,4) and B (4,8), which of the following represents the slope of AB ?
A. 2
B.
2
3
C.
2
3
D.
3
2
2. Given points A (3,-3) and B (2,-5), which of the following represents the slope of AB ?
A. 2
B.-8
C.-2
D.8
3. Given points A (-7,3) and B (-1,1), which of the following represents the slope of AB ?
A. 3
B. -3
C.
1
3
D.
1
3
4.The line 3x – 4y = 12 has a:
A. Positive Slope
B. Negative Slope
C. Zero Slope
D. Undefined Slope
B. Negative Slope
C. Zero Slope
D. Undefined Slope
B. Negative Slope
C. Zero Slope
D. Undefined Slope
B. Negative Slope
C. Zero Slope
D. Undefined Slope
B. Negative Slope
C. Zero Slope
D. Undefined Slope
5.The line x = 7 has a:
A. Positive Slope
6.The line -4y = 8x + 40 has a:
A. Positive Slope
7.The line y = -5 has a:
A. Positive Slope
8.The line 5x + 7y = -14 has a:
A. Positive Slope
9. The equation of the line that has a slope of 5 and goes through (1,-2) is:
A. y = 5x + 1
B. y = 5x - 7
C. y = 5x + 3
D. y = 5x – 2
10. The equation of the line that has a slope of -1 and goes through (-3,0) is:
A. y = -1x
B. y = -1x - 3
C. y = -1x + 3
D. y = 1x – 3
12. Which of the following equations has a slope of 2 and a y intercept of -3
A. y = -2x - 3
B. 2x – y + 3 = 0
C. 6 = 4x – 2y
D. y – 2x = 3
13. How solutions would occur when you graph, y = 2x – 1 and 4x – 2y = 12?
A. None
B. One
C. Two
D. Infinite
Linear Equations Reveiw
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14. How solutions would occur when you graph, y = 2x – 1 and x + 2y = 4?
A. None
B. One
C. Two
D. Infinite
15. How solutions would occur when you graph, y = x – 1 and x + y – 2 = 0?
A. None
B. One
C. Two
D. Infinite
Determine whether the following are (T)rue or (F)alse. If False tell why!
16. A positive slope rises to the right.
T or F
17. A negative slope falls to the left.
T or F
18. Slope is the rise over the run.
T or F
19. y = 3x – 8 has a positive slope
T or F
20. y – 6 = 5(x – 9) has a negative slope.
T or F
21. 3x + 4y = 12 has a negative slope.
T or F
22. -4y = 8x – 3 has a negative slope.
T or F
23. The slope of x = -3 is zero.
T or F
24. If A (-3,5) and B (-5,7), then the slope of AB is -1.
T or F
25. If A (2,3) and B (4,9), then the slope of AB is 3.
T or F
26. If A (-1,4) and B (5,5), then the slope of AB is
1
.
6
T or F
27. The equation of a vertical line through point A (-4,8) is x = -4.
T or F
28. The equation of a vertical line through point A (-2,-5) is x = -5.
T or F
29. The equation of a horizontal line through point A (–1,3) is y = 3.
T or F
30. The equation of a horizontal line through point A (3,9) is y = -9.
T or F
31. Write the equation of a line in slope intercept form.
a) m = 2 (3,5)
b) m = -4 (4,0)
c) m = 
3
5
(5,6)
Linear Equations Reveiw
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32. Write the equation of a line in slope intercept form.
a)
b)
_____________________
_____________________
33. Write the equation of a line in point slope form.
2
b) m = 
(6,3)
a) m = 2 (-3,-1)
3
________________________
________________________
34. Determine the x and y intercepts of the line.
a) 2x – 5y = 20
b) y = 1x - 3
( ____ , 0)
(0, _____)
( ____ , 0)
35. Graph the following lines
a) y = 2x + 1 and y – 1 = -3 (x – 3)
b) y =
c)
________________________
c) m = -5
(-7,3)
________________________
c) 3x - 2y = 18
(0, _____)
2
3
x -5 and y =
x+7
3
2
( ____ , 0)
(0, _____)
c) 2x - 3y = 6 and 3x + 2y = 18
Linear Equations Reveiw
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36. Determine if the following systems of linear equations have (O)ne Solution, (N)o Solutiion or (I)nfinite
Solutions.
a)
b)
c)
y  3x  8
2 y  x  2
y  3x  5
3y  x  2
1
3x  y   2
y x4
2
O or N or I
O or N or I
O or N or I
37. Solve the system of equations.
a)
y  7 x  11
b)
1x  2 y  1
y  5x  5
2 x  3 y  3
c)
d)
1
x5
2
3
y   x5
4
y
5 x  4 y  8
2 x  4 y  20
Linear Equations Reveiw
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38. a) Determine the coordinate(s) of any points of
intersection between the circle ( x  1) 2   y  1  25
2
and
the line, y = 2x - 2.
b) After determining the points of intersection, now
graph the circle and the line to confirm your
calculations.