20 to 16 percent error
1 answer:
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Answer:
The given table is
Hours. Earnings per hour.
0
4
8
12
Now, the unit rate is $8.25 per hour, according to the proble, this is the constant ratio of change, that means, we only need to multiply the number of hours with the unit rate.
Hours. Earnings per hour.
0 0
4 33
8 66
12 99
Problem 13a
Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.
Another point on this line is (3,8) which is drawn from the second column.
Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2
Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2
Plug those into y = mx+b and we get y = 2x+2
Answer: y = 2x+2
==============================================
Problem 13b
(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20
Another point on this line is (3,8) as drawn from the second column
Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4
Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20
Answer: y = -4x+20
==============================================
Problem 13c
(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.
Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5
Note: the fraction 3/2 is equivalent to the decimal form 1.5
Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2
So we can now update y = mx+b to y = 1.5x+2
Answer: y = 1.5x+2
Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write
==============================================
Problem 13d
(0,20) is on the line. So the y intercept is 20, indicating that b = 20
(3,11) is also on the line
Again as done with 13a-13c, I'm only looking at the first two columns.
Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3
Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier
Answer: y = -3x+20
Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.
Another point on this line is (3,8) which is drawn from the second column.
Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2
Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2
Plug those into y = mx+b and we get y = 2x+2
Answer: y = 2x+2
==============================================
Problem 13b
(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20
Another point on this line is (3,8) as drawn from the second column
Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4
Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20
Answer: y = -4x+20
==============================================
Problem 13c
(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.
Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5
Note: the fraction 3/2 is equivalent to the decimal form 1.5
Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2
So we can now update y = mx+b to y = 1.5x+2
Answer: y = 1.5x+2
Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write
==============================================
Problem 13d
(0,20) is on the line. So the y intercept is 20, indicating that b = 20
(3,11) is also on the line
Again as done with 13a-13c, I'm only looking at the first two columns.
Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3
Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier
Answer: y = -3x+20
Answer:
Step-by-step explanation:
The first step is to multiply the numbers of the numerator. Thus:
Writing the answer above as the product of a whole number and unit fraction (that is, mixed number), 5 goes in 8 1 time remainder 3. Therefore: