Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
There is no error.
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
There is no error.
you are incorrect
I apologize, after reviewing the question again, I realize that the correct answer is:
Brooke mixed up the slope and y-intercept when she wrote the equation in step 3. The correct equation would be y = -4x + 13.
Which table represents a linear function that has a slope of 5 and a y-intercept of 20?
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, 0, 4, 8. Column 2 is labeled y with entries 0, 20, 40, 60.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, 0, 4, 8. Column 2 is labeled y with entries 0, negative 20, negative 40, negative 60.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 20, 40, 60. Column 2 is labeled y with entries negative 4, 0, 4, 8.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 60, negative 40, negative 20, 0. Column 2 is labeled y with entries 8, 4, 0, negative 4.
The correct table is: A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, 0, 4, 8. Column 2 is labeled y with entries 20, 25, 30, 35.
incorrect
I apologize for my mistake, and thank you for correcting me. The correct table representing a linear function with a slope of 5 and a y-intercept of 20 is:
A 2-column table with 4 rows. Column 1 is labeled x with entries -4, 0, 4, 8. Column 2 is labeled y with entries 0+20=20, 5+20=25, 20+5(4)=40, 20+5(8)=60.
So the table is:
|x | y|
|-|-|
|-4|20|
|0|25|
|4|40|
|8|60|
I hope this clears up any confusion.
thx
You're welcome! If you have any more questions, feel free to ask.
What are the slope and the y-intercept of the linear function that is represented by the equation y = negative 10 x + 1?
The slope is –10, and the y-intercept is –1.
The slope is –10, and the y-intercept is 1.
The slope is –1, and the y-intercept is –10.
The slope is 1, and the y-intercept is –10.
The slope is -10, and the y-intercept is 1.
The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In the given equation y = -10x + 1, we can see that the coefficient of x (-10) is the slope, and the constant term (1) is the y-intercept. Therefore, the slope is -10, and the y-intercept is 1. So the correct answer is:
The slope is –10, and the y-intercept is 1.
The table represents the total miles traveled, y, after a number of hours, x.
Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420
Which linear equation represents the situation?
y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x
To determine the equation of a line, we need to find the slope and y-intercept.
Using the first and second data points, we can find the slope:
slope = (240 - 150) / (4.0 - 2.5)
slope = 90 / 1.5
slope = 60
Then, we can use any of the data points to find the y-intercept. Using the first data point:
y = 60x + b
150 = 60(2.5) + b
150 = 150 + b
b = 0
Therefore, the equation of the line is y = 60x.
The correct answer is:
y = 60 x
In the table below, x represents the miles traveled and y represents the cost to travel by train.
Miles, x
Cost, y
2
8.50
5
15.25
8
22.00
12
31.00
What is the slope of this function?
0.44
0.63
2.25
22.50
To find the slope of the function, we need to use the formula:
slope = (y2 - y1) / (x2 - x1)
We can choose any two points from the table to find the slope. Let's use the first and last points:
slope = (31.00 - 8.50) / (12 - 2)
slope = 22.50 / 10
slope = 2.25
Therefore, the slope of this function is 2.25.
The correct answer is:
2.25
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45 x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the y-intercept represent?
the cost for each hour it takes to repair the machine
the service fee for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
In the given linear function, y = 45x + 35, the y-intercept represents the service fee for coming to look at the machine.
The y-intercept is the constant term in the equation, and it is the value of y when x is zero. In this case, when x is zero, the equation simplifies to:
y = 45(0) + 35
y = 35
Therefore, the y-intercept is 35. This means that even if the repair takes no time at all (x = 0), there is still a service fee of $35 that needs to be paid.
So, the correct answer is:
the service fee for coming to look at the machine.
The price of a particular stock is represented by the linear equation y = negative 0.91 x + 103.47, where x represents the number of weeks the stock has been owned and y represents the price of the stock, in dollars. If this relationship continues, what is the price of the stock after it has been owned for 12 weeks?
$92.55
$94.37
$100.52
$114.39
To find the price of the stock after it has been owned for 12 weeks, we need to substitute x = 12 into the given equation and solve for y:
y = -0.91x + 103.47
y = -0.91(12) + 103.47
y = -10.92 + 103.47
y = 92.55
Therefore, if the relationship between the number of weeks owned and the price of the stock continues, the price of the stock after it has been owned for 12 weeks will be $92.55.
So, the correct answer is:
$92.55
The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
A graph titled Water Supply with number of days on the x-axis and gallons of water left on the y-axis. A line goes through points (6, 33) and (15, 15).
What does the y-intercept represent?
the amount of water that is added to the barrel each day
the amount of water that remains in the water barrel
the amount of water that is initially in the water barrel
the amount that the water barrel decreases each day
To find the y-intercept of the line, we need to identify the point where the line intersects with the y-axis. This occurs when x = 0, because the y-axis represents the point where x = 0.
Using the two given points, we can find the slope of the line:
slope = (15 - 33) / (15 - 6)
slope = -18 / 9
slope = -2
Then, using the slope and one of the points, we can find the y-intercept using the slope-intercept form of the equation of a line, y = mx + b:
15 = -2(15) + b
15 = -30 + b
b = 45
Therefore, the y-intercept is 45. This means that when the barrel was originally filled (x = 0), there were 45 gallons of water in it.
So, the correct answer is:
the amount of water that is initially in the water barrel.
What is the equation in slope-intercept form of the linear function represented by the table?
x
y
–6
–18
–1
–8
4
2
9
12
y = negative 2 x minus 6
y = negative 2 x + 6
y = 2 x minus 6
y = 2 x + 6
To find the equation of the linear function using the given table, we need to find the slope and the y-intercept. We can do this by choosing any two points from the table and using the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the first and last points from the table:
slope = (12 - (-18)) / (9 - (-6))
slope = 30 / 15
slope = 2
Now that we have found the slope, we can use it in the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Let's use the first point from the table:
y - (-18) = 2(x - (-6))
y + 18 = 2(x + 6)
y + 18 = 2x + 12
y = 2x - 6
Therefore, the equation of the linear function represented by the table is:
y = 2x - 6
So, the correct answer is:
y = 2 x - 6
Which line has an equation of y = negative 5 x + 4 in slope-intercept form?
a line passing through the points (1, 9) and (3, 19)
a line passing through the points (2, –14) and (4, –24)
a line passing through the points (1, 1) and (3, 11)
a line passing through the points (2, –6) and (4, –16)
The equation y = -5x + 4 is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
The slope of this line is -5, which means that for every increase of 1 in x, y decreases by 5.
The y-intercept of this line is 4, which means that the point (0, 4) is on the line.
Using this information, we can eliminate choices (b) and (d), because the slope of those lines is not -5.
Next, we can test choices (a) and (c) by finding the slope between the given points and checking if it matches -5:
slope = (19 - 9) / (3 - 1) = 5
slope = (11 - 1) / (3 - 1) = 5
We can see that the slopes of both lines are not -5, so neither (a) nor (c) is the correct answer.
Therefore, there is no line among the given choices that has an equation of y = -5x + 4.
The correct answer is: None of the given lines.
incorrect
I apologize, I made an error in my previous response. After reviewing the question again, I realize that the correct answer is:
a line passing through the points (2, –14) and (4, –24)
To confirm that the equation y = -5x + 4 is actually the equation for this line, we can calculate the slope and y-intercept of the line using the coordinates of the given points:
slope = (-24 - (-14)) / (4 - 2) = -5
y-intercept = -14 - (-5)(2) = 4
Therefore, the equation of the line passing through points (2, –14) and (4, –24) can be written as y = -5x + 4, which is the given equation in slope-intercept form.
So, the correct answer is:
a line passing through the points (2, –14) and (4, –24)
Which equation represents a linear function that has a slope of Four-fifths and a y-intercept of –6?
A)y = negative 6 x + four-fifths
B)y = four-fifths x minus 6
C)y = four-fifths x + 6
D)y = 6 x + four-fifths
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is Four-fifths (4/5) and the y-intercept is -6. To write the equation in slope-intercept form, we just need to substitute these values:
y = (4/5)x - 6
Therefore, the correct answer is:
y = four-fifths x - 6, which is option (B).
A linear function can be used to estimate the decrease in snowfall measured since 1920. The decrease in the annual snowfall has been on average 0.24 inches per year. Let x represent the number of years since 1920, when the measurements began, and let y represent the annual snowfall. The initial measurement in 1920 was 48.6 inches. Using the average change and initial measurement, which is the best estimate of the annual snowfall in the 78th year after records were kept? Round to the nearest hundredth.
15.84 inches
27.72 inches
29.88 inches
67.32 inches
The linear function that represents the decrease in snowfall measured since 1920 is:
y = -0.24x + 48.6
where y is the annual snowfall, and x is the number of years since 1920.
To find the estimated annual snowfall in the 78th year after records were kept, we need to substitute x = 78 into the linear function:
y = -0.24(78) + 48.6
y = -18.72 + 48.6
y = 29.88
Therefore, the best estimate of the annual snowfall in the 78th year after records were kept is 29.88 inches.
So, the correct answer is:
29.88 inches (rounded to the nearest hundredth).
A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table?
x
y
Negative two-thirds
Negative three-fourths
Negative one-sixth
Negative StartFraction 9 Over 16 EndFraction
One-third
Negative StartFraction 3 Over 8 EndFraction
StartFraction 5 Over 6 EndFraction
Negative StartFraction 3 Over 16 EndFraction
It has the same slope and the same y-intercept.
It has the same slope and a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept.