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