Coordinates and trigonometry · Ages 14–15

Slope worksheet

Part of: Coordinate geometry

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Coordinates and trigonometry · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Read A and B off the picture. The slope of the line AB =
Answer in simplest form
Answer:
2.The slope of the line through A(−3, −3) and B(5, −5) =
Answer in simplest form
Answer:
3.The slope of the line through A(−3, 6) and B(−4, −3) =
Answer in simplest form
Answer:
4.A line passes through A(6, −4) and B(4, −3). From A to B, y changes by and x by , so the slope = .
Fill in each blank
Answer:
5.A line passes through A(6, 1) and B(−5, 5). From A to B, y changes by and x by , so the slope = .
Fill in each blank
Answer:
6.A line passes through P(−3, 4) and Q(1, −12). Its slope =
Answer in simplest form
Answer:
7.A line passes through P(−6, 11) and Q(−4, 2). Its slope =
Answer in simplest form
Answer:

8.What is the slope of the line through A(2, 4) and B(3, 4)?
- A. Undefined
- B. 0
- C. Positive
- D. Negative
Choose the right answer
Answer:
9.What is the slope of the line through A(−2, −6) and B(3, −6)?
- A. Negative
- B. Undefined
- C. Positive
- D. 0
Choose the right answer
Answer:
10.The line through A(1, −3) and B(6, −6) has slope 35.
True or false?
Answer:
11.The line through A(−2, 6) and B(2, 3) has slope −34.
True or false?
Answer:
12.A line of slope 3 is steeper than a line of slope −4.
True or false?
Answer:

13.A straight stretch of road starts 35 m above sea level and ends 46 m above it, 50 m apart across. Measured from start to end, what is its slope?
Answer in simplest form
Working:
Answer:
14.Four ramps: ramp 1 rises 1 m over 13 m across; ramp 2 rises 1 m over 10 m; ramp 3 rises 5 m over 30 m; ramp 4 rises 3 m over 26 m. Which is steepest?
- A. Ramp 2
- B. Ramp 1
- C. Ramp 4
- D. Ramp 3
Choose the right answer
Working:
Answer:
15.With the ground as the x-axis (in m), a straight ramp rises from A(2, 0) on the ground to the door at D(−11, 3). From A to D, y changes by and x by , and the ramp's slope = .
Fill in each blank
Working:
Answer:
16.A wheelchair ramp rises 1.5 m over 29 m across. Ramps may have a slope of at most 112; this one meets the rule.
True or false?
Working:
Answer:
17.With the ground as the x-axis (in m), a straight ramp rises from A(2, 0) on the ground to the door at D(10, 3). From A to D, y changes by and x by , and the ramp's slope = .
Fill in each blank
Working:
Answer:
18.A straight stretch of road starts 36 m above sea level and ends 56 m above it, 150 m apart across. Measured from start to end, what is its slope?
Answer in simplest form
Working:
Answer:

Show the answers and working

Slope worksheet: Answers and working

1. −65
A(−4, 6), B(6, −6): from A to B the rise is −12 and the run 10, so the slope = −1210 = −65.
2. −14
Slope = −5 − (−3)5 − (−3) = −28 = −14. Subtract in the same order on top and below.
3. 9
Slope = −3 − (6)−4 − (−3) = −9−1 = 91. Subtract in the same order on top and below.
4. 1, −2, −12
y: −3 − (−4) = 1; x: 4 − (6) = −2; slope = 1−2 = −12 (in simplest form).
5. 4, −11, −411
y: 5 − (1) = 4; x: −5 − (6) = −11; slope = 4−11 = −411 (in simplest form).
6. −4
Slope = 4 − (−12)−3 − (1) = 16−4 = −41; Q minus P gives the same.
7. −92
Slope = 11 − (2)−6 − (−4) = 9−2 = −92; Q minus P gives the same.

8. B. 0
Look at 4 − (4)3 − (2): same signs, positive; opposite, negative; 0 on top, a slope of 0; 0 below, no slope is defined.
9. D. 0
Look at −6 − (−6)3 − (−2): same signs, positive; opposite, negative; 0 on top, a slope of 0; 0 below, no slope is defined.
10. False
Slope = −6 − (−3)6 − (1) = −35 = −35. Mind the sign: subtract in the same order on top and below.
11. True
Slope = 3 − (6)2 − (−2) = −34 = −34. Mind the sign: subtract in the same order on top and below.
12. False
Steepness is the slope's size, not its sign: for each 1 across, one line rises or falls 3, the other 4.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 1150
Slope = change in height ÷ distance across = 46 − 3550 = 1150 = 1150. Downhill is negative.
14. D. Ramp 3
Slope = rise ÷ run: 113, 110, 530, 326; the biggest is steepest. Compare them as decimals or over a common denominator.
15. 3, −13, −313
y: 3 − 0 = 3; x: −11 − (2) = −13; slope = 3−13 = −313.
16. True
Slope = 1.5 ÷ 29 = 358; compare it with 112, or see whether 29 is at least 12 times 1.5.
17. 3, 8, 38
y: 3 − 0 = 3; x: 10 − (2) = 8; slope = 38 = 38.
18. 215
Slope = change in height ÷ distance across = 56 − 36150 = 20150 = 215. Downhill is negative.

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