1 of 8 · prop-graphs-c01
y = 9x. When x = 7, y = ?
- The equation y = 9x means y is 9 times x.
- The question gives x = 7, so put 7 in for x.
- 9 times 7 is 63.
- You multiply because 9 is the rate and 7 is how many.
- So y is 63.
Answer: 63
Solution key: Four ways to say the same thing
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Camp · Four ways to say the same thing
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2 of 8 · prop-graphs-c02
A proportional table: x = 1,2,3 and y = 6,12,18. Write k.
- k is y divided by x, and it should match every row.
- When x is 1, y is 6, so 6 divided by 1 is 6.
- Check the other rows: 12 divided by 2 is 6, and 18 divided by 3 is 6.
- Every row gives the same 6, so the rate is constant.
- So k is 6.
Answer: 6
3 of 8 · prop-graphs-c03
d = 55t, where d is miles and t is hours. Distance after 4 hours?
- d = 55t means distance equals 55 miles each hour times the number of hours.
- Here the time is 4 hours.
- 55 times 4 is 220.
- You multiply speed by time to get distance.
- So the distance is 220 miles.
Answer: 220 miles
4 of 8 · prop-graphs-c04
A straight proportional graph through (0,0) and (5, 40). Equation is y = kx. k = ?
- The straight line goes through (0, 0), so it represents a proportional relationship, y = kx. It also passes through (5, 40).
- k is y divided by x at the point you can read.
- 40 divided by 5 is 8.
- That means 8 units of y for each 1 unit of x.
- So k is 8.
Answer: 8
5 of 8 · prop-graphs-c05
If y = 3x, what is y when x = 0?
- y = 3x means y is 3 times x, with no number added on.
- Put 0 in for x, because the question asks about that moment.
- 3 times 0 is 0.
- The graph of a proportional relationship passes through the origin, (0, 0), where both coordinates are zero.
- So y is 0.
Answer: 0
6 of 8 · prop-graphs-c06
A sentence: 'Pay is $15 per hour.' Equation for pay y after x hours: y = ? x. What number goes in front of x?
- The sentence says pay is $15 for each hour, with no extra fee.
- In y = kx, the number in front of x is that unit rate.
- Hours are x and pay is y, so you multiply hours by 15.
- Nothing is added, because there is no start fee.
- So the number in front of x is 15.
Answer: 15
7 of 8 · prop-graphs-c07
In y = kx, x = 8 and k = 2.5. What is y?
- y = kx, so multiply k by x.
- k is 2.5 and x is 8.
- 2 times 8 is 16, and 0.5 times 8 is 4.
- 16 plus 4 is 20.
- So y is 20.
Answer: 20
8 of 8 · prop-graphs-c08
A line through (0,0) and (10, 7). k as a decimal?
- k is y divided by x for a point on the line.
- Use (10, 7), because (0, 0) does not give a rate.
- 7 divided by 10 is 0.7.
- That is the same as the fraction 7/10.
- So k is 0.7.
Answer: 0.7
Four ways to say the same thing · Camp
1 of 8 · prop-graphs-c01
y = 9x. When x = 7, y = ?
- The equation y = 9x means y is 9 times x.
- The question gives x = 7, so put 7 in for x.
- 9 times 7 is 63.
- You multiply because 9 is the rate and 7 is how many.
- So y is 63.
Answer: 63
2 of 8 · prop-graphs-c02
A proportional table: x = 1,2,3 and y = 6,12,18. Write k.
- k is y divided by x, and it should match every row.
- When x is 1, y is 6, so 6 divided by 1 is 6.
- Check the other rows: 12 divided by 2 is 6, and 18 divided by 3 is 6.
- Every row gives the same 6, so the rate is constant.
- So k is 6.
Answer: 6
3 of 8 · prop-graphs-c03
d = 55t, where d is miles and t is hours. Distance after 4 hours?
- d = 55t means distance equals 55 miles each hour times the number of hours.
- Here the time is 4 hours.
- 55 times 4 is 220.
- You multiply speed by time to get distance.
- So the distance is 220 miles.
Answer: 220 miles
4 of 8 · prop-graphs-c04
A straight proportional graph through (0,0) and (5, 40). Equation is y = kx. k = ?
- The straight line goes through (0, 0), so it represents a proportional relationship, y = kx. It also passes through (5, 40).
- k is y divided by x at the point you can read.
- 40 divided by 5 is 8.
- That means 8 units of y for each 1 unit of x.
- So k is 8.
Answer: 8
5 of 8 · prop-graphs-c05
If y = 3x, what is y when x = 0?
- y = 3x means y is 3 times x, with no number added on.
- Put 0 in for x, because the question asks about that moment.
- 3 times 0 is 0.
- The graph of a proportional relationship passes through the origin, (0, 0), where both coordinates are zero.
- So y is 0.
Answer: 0
6 of 8 · prop-graphs-c06
A sentence: 'Pay is $15 per hour.' Equation for pay y after x hours: y = ? x. What number goes in front of x?
- The sentence says pay is $15 for each hour, with no extra fee.
- In y = kx, the number in front of x is that unit rate.
- Hours are x and pay is y, so you multiply hours by 15.
- Nothing is added, because there is no start fee.
- So the number in front of x is 15.
Answer: 15
7 of 8 · prop-graphs-c07
In y = kx, x = 8 and k = 2.5. What is y?
- y = kx, so multiply k by x.
- k is 2.5 and x is 8.
- 2 times 8 is 16, and 0.5 times 8 is 4.
- 16 plus 4 is 20.
- So y is 20.
Answer: 20
8 of 8 · prop-graphs-c08
A line through (0,0) and (10, 7). k as a decimal?
- k is y divided by x for a point on the line.
- Use (10, 7), because (0, 0) does not give a rate.
- 7 divided by 10 is 0.7.
- That is the same as the fraction 7/10.
- So k is 0.7.
Answer: 0.7