The value of a baseball card can be represented by the equation y = 3 x + 39, where x represents the number of years that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39
The value of the card when Robert originally purchased it can be found by setting x = 0 in the equation y = 3x + 39. This gives:
y = 3(0) + 39
y = 39
Therefore, the value of the card when Robert originally purchased it was $39. Answer: $\boxed{\$39}$.
A local public library decides to track the number of hours that a certain computer is being used. The table represents the number of hours, y, which is dependent on the number of days, x.
x
y
3
21
5
37
7
53
What is the linear equation that represents this situation?
y = 8 x + 45
y = 8 x minus 3
y = 2 x + 16
y = 2 x minus 32
Mark this and return
We can find the equation by first finding the slope and y-intercept. Using the values given in the table:
Slope = (Change in y) / (Change in x) = (53 - 21) / (7 - 3) = 8
y-intercept = y - mx = 21 - 8(3) = -3
Therefore, the equation that represents the situation is:
y = 8x - 3
Hence, the answer is: $\boxed{y = 8x - 3}$.
What can be concluded about a line that passes through the points (1, negative 2) and (4, negative 2)? Check all that apply.
The slope is 0.
The y-intercept is Negative 2.
The line is vertical.
The line is horizontal.
The line has no y-intercept.
The equation of the line is y = negative 2.
The two points have the same y-coordinate, which means the line is horizontal. Also, since the y-coordinate of any point on this line is -2, the equation of the line is y = -2. Therefore, the correct options are:
- The slope is 0.
- The y-intercept is Negative 2.
- The line is horizontal.
- The equation of the line is y = negative 2.
So the answer is:
- The slope is 0.
- The y-intercept is Negative 2.
- The line is horizontal.
- The equation of the line is y = negative 2.
What are the slope and the y-intercept of the linear function that is represented by the table?
x
y
–1
Negative three-halves
Negative one-half
0
0
Three-halves
One-half
3
The slope is –3, and the y-intercept is Negative one-half.
The slope is –3, and the y-intercept is Three-halves.
The slope is 3, and the y-intercept is Negative one-half.
The slope is 3, and the y-intercept is Three-halves.
To find the slope of a linear function given a table of values, we need to use the formula:
slope = (change in y) / (change in x).
Selecting two points from the table, we find:
slope = (0 - (-3/2)) / (0 - (-1/2)) = (-3/2) / (1/2) = -3.
Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Choosing any of the points from the table, (0, 0) for example, we can substitute the slope and the coordinates into the equation:
y - 0 = -3(x - 0)
y = -3x
Therefore, the slope is -3 and the y-intercept is 0, which is not given as one of the answer choices. However, we can rewrite the equation as:
y = -3x + 0
This shows that the y-intercept is 0. Therefore, the correct answer is:
The slope is -3, and the y-intercept is 0.
choose the correct awnser choixe The slope is –3, and the y-intercept is Negative one-half.
The slope is –3, and the y-intercept is Three-halves.
The slope is 3, and the y-intercept is Negative one-half.
The slope is 3, and the y-intercept is Three-halves.
The correct answer choice is:
The slope is -3, and the y-intercept is 0.
This is because we found the slope to be -3 and the y-intercept to be 0 in the previous solution. None of the answer choices given match this result exactly. However, we can see that the answer choice "The slope is –3, and the y-intercept is Negative one-half" has the same slope as our calculation, but the y-intercept is incorrect.
The number of pounds of dog food that a pet store has is represented by the equation y = negative 15 x + 430, where x represents the number of days that the store is open and y represents the pounds of dog food in stock in the store. How many pounds of dog food will the pet store have after 21 days?
92
115
315
336
To find the number of pounds of dog food after 21 days, we can substitute x = 21 into the equation:
y = -15(21) + 430 = -315 + 430 = 115
Therefore, the pet store will have 115 pounds of dog food after 21 days. Answer: $\boxed{115}$.
Which equation represents the line that passes through points (0, 6) and (2, 0)?
y = negative one-third x + 2
y = negative one-third x + 6
y = negative 3 x + 2
y = negative 3 x + 6
To find the equation of the line that passes through two given points, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the points. Selecting the two given points, we have:
x1 = 0, y1 = 6
x2 = 2, y2 = 0
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - 6) / (2 - 0) = -3
Substituting the slope and one of the points into the point-slope form, we get:
y - 6 = -3(x - 0)
Simplifying:
y - 6 = -3x
y = -3x + 6
Therefore, the correct equation that represents the line passing through the two points is:
y = -3x + 6
Hence, the answer is $\boxed{y = -3x + 6}$.
Inez has a phone card. The graph shows the number of minutes that remain on her phone card after a certain number of days.
A graph titled Phone Card Balance has Number of Days on the x-axis, and Number of Minutes Remaining on the y-axis. A line goes through points (2, 750) and (8, 450).
The slope of the line that represents the data is –50, and the y-intercept is 850. What do the slope and y-intercept represent in Inez’s situation?
The y-intercept indicates that the phone card started with 850 minutes. The slope indicates that 50 minutes were used per day.
The y-intercept indicates that the phone card started with 50 minutes. The slope indicates that 850 minutes were used per day.
The slope indicates that the phone card started with 850 minutes. The y-intercept indicates that 50 minutes were added per day.
The slope indicates that the phone card started with 50 minutes. The y-intercept indicates that 850 minutes were added per day.
The correct statement is:
The y-intercept indicates that the phone card started with 850 minutes. The slope indicates that 50 minutes were used per day.
The slope of -50 means that for every one day that passes, 50 minutes are subtracted from the phone card balance. The negative slope indicates a decrease in minutes.
The y-intercept of 850 means that when the number of days equal to zero, the phone card balance was 850 minutes. In other words, the phone card started with 850 minutes.
Therefore, the correct option is:
The y-intercept indicates that the phone card started with 850 minutes. The slope indicates that 50 minutes were used per day.
Which equation represents the line that passes through points B and C on the graph?
On a coordinate plane, point A is at (1, 4), point B is at (negative 4, 2), point C is at (negative 2, negative 2) and point D is at (5, negative 4).
y = negative 2 x minus 6
y = negative 2 x + 10
y = 2 x minus 6
y = 2 x + 10
To find the equation of the line that passes through two given points, we need to first find the slope of the line. Using points B and C given in the problem, we can find the slope of the line passing through them using the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = B and (x2, y2) = C.
slope = (-2 - 2) / (-2 - (-4)) = -4 / 2 = -2
This gives us the slope of the line. Using point-slope form of a line with the slope we just calculated and one of the points (for example, point B) we get:
y - y1 = m(x - x1)
y - 2 = -2(x - (-4))
y - 2 = -2(x + 4)
y - 2 = -2x - 8
y = -2x - 6
Therefore, the correct equation that represents the line passing through points B and C is:
y = -2x - 6
Hence, the answer is $\boxed{y = -2x - 6}$.
Jill converted the equation of the line 15 x minus 14 y = negative 2 into slope-intercept form and found the slope and y-intercept of the line as follows.
15 x minus 14 y = negative 2. 15 x minus 4 y minus 15 x = negative 2 minus 15 x. negative 4 y = negative 2 minus 15 x. StartFraction negative 4 y Over negative 4 EndFraction = StartFraction negative 2 minus 15 x Over negative 4 EndFraction. Y = StartFraction negative 2 Over negative 4 EndFraction minus StartFraction 15 x Over negative 4 EndFraction. y = one-half minus StartFraction 15 Over 4 EndFraction x. y = negative StartFraction 15 Over 4 EndFraction x + one-half. slope = negative StartFraction 15 Over 4 EndFraction. y-intercept = one-half.
What was her mistake?
She mixed up the slope and the y-intercept.
She got the sign of the slope wrong.
She got the sign of the y-intercept wrong.
She found the reciprocals of the slope and the y-intercept.
The answer is:
She got the sign of the slope wrong.
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept. In the solution provided, Jill found the equation of the line correctly but made an error when simplifying by dividing both sides by -4. The step should result in:
y = (15/4)x - 1/2
This shows that the slope is positive 15/4 (not negative), which means the correct answer is:
She got the sign of the slope wrong.
Therefore, her mistake was getting the sign of the slope wrong.
The equation of the line that passes through points (0, negative 7) and (2, negative 1) is shown below. What value is missing from the equation?
y =
x – 7
To find the full equation of the line passing through the given two points, we need to first find the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, -7) and (x2, y2) = (2, -1).
slope = (-1 - (-7)) / (2 - 0) = 6 / 2 = 3
This gives us the slope of the line. Using point-slope form of a line with the slope we just calculated and one of the points (for example, point (0, -7)) we get:
y - y1 = m(x - x1)
y - (-7) = 3(x - 0)
y + 7 = 3x
y = 3x - 7
Therefore, the equation of the line passing through points (0, -7) and (2, -1) is:
y = 3x - 7
Hence, the missing value in the given equation is $\boxed{3}$.