ANSWERS MATH 10 REVIEW of LINES
Key Concepts: slope, intercepts (x-intercept and y-intercept), coordinate system, quadrants, slope formula, graphing from a table, graphing from slope and y-intercept, finding the slope of a line, standard form, slope y-intercept form, parallel and perpendicular lines
WARM-UP You should be able to answer the following quickly:
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Part A |
Part B |
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What is the slope of: y = 4x – 3? 4 What is the y-intercept of y = 4x – 3? -3 What is the slope of the line parallel to What is the slope of the line perpendicular to Find the slope of the line through (2,5) and
(5,11)? 2 What is the equation of the line with slope 7 and
y-intercept 3? y=7x+3 What is the x-intercept of 3x + 5y = 12? 4 What is the y-intercept of 3x + 5y = 20? 4 What is the slope of the line y=3? 0 What is the y-intercept of the line |
What is the slope of: y = 7x – 3? 7 What is the y-intercept of y = 4x + 9? 9 What is the slope of the line parallel to What is the slope of the line perpendicular to Find the slope of the line through (1,1) and
(13,5)? 1/2 What is the equation of the line with slope 3 and
y-intercept 5? y=3x+5 What is the x-intercept of 4x + 3y = 12? 4 What is the y-intercept of 5x + 3y = 15? 5 What is the slope of the line x=3? undefined What is the y-intercept of the line |
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A. Change to standard form:
2x–3y = 7 x–3y = -10 3x –
9y = –2
B. Change to slope y-intercept form
3x
– 2y = 6 x
+ 3y = 8
y = -2x – 4 y = 3/2 x – 3 y = -1/3
x + 8/3
C.
Graph using the slope and intercept: 
D. Make a table and graph 3x + 2y = 5
E. Graph using intercepts 2x + 3y = 6
F. Find the equation of a line:
1. With slope 5 and y-intercept 7. With slope –2/3 and y-intercept 9
y = 5x + 7 y
= -2/3 x +9
2. Given x-intercept = 3, and y-intercept = 2 Given x-intercept = -5, and y-intercept = 3
y = -2/3 x + 2 y
= 3/5 x + 3
3. With slope 3; through (2,5) With slope 2/3 through (5,–2)
y = 3x + b y
= 2/3 x + b
5 = 3(2) + b -2 =
2/3 (5) + b
5 = 6 + b b
= -2 – 10/3 = -6/3 – 10/3 = -16/3
b = -1 y
= 2/3 x – 16/3
y = 3x – 1
4. Through (1,4) and (4,-2) Through (5,-2) and (7,5)
m = (-2-4)/(4-1) = -6/3 = -2 m = 7/2
y = -2x + b -2
= 7/2 (5) + b
4 = -2(1) + b b =
-2 – 35/2 = -39/2
b = 6
y = -2x + 6 y
= 7/2 x – 39/2
5. Parallel to 3x + 4y = –16 and through (5,5)
This line has slope –3/4. Any line parallel to it has slope –3/4 and
looks like:
3x + 4y = ????. Substitute in the point (5,5) to get 3(5) +
4(5) = 35
3x + 4y = 35
6. Perpendicular to 5x + 2y = 10 and through (5,5).
This line has slope –5/2. The line perpendicular to it has slope +2/5
(negative reciprocal).
The line we are looking for is 2x –
5y = ____. Substitute in 2(5) – 5(5) =
-15
2x – 5y = -15