What is the x-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 4).
(–2, 0)
(–1, 2)
(0, 4)
(4, 0)
The x-intercept is the point where the line crosses the x-axis, meaning the y-coordinate is 0. Looking at the given points, we can see that the x-coordinate is -2 when the y-coordinate is 0. Therefore, the x-intercept is (-2, 0). Answer: (–2, 0)
Which statement matches the graph that is shown below?
On a coordinate plane, a line goes through points (0, 4) and (8, 0).
The y-intercept is 4.
The x-intercept is 0.
A savings account started with $8 in it.
It took 4 minutes to run a mile.
The statement that matches the graph is:
On a coordinate plane, a line goes through points (0, 4) and (8, 0).
Which statement could be an interpretation of the graph’s x-intercept or y-intercept?
On a coordinate plane, a line goes through points (0, 800) and (400, 0).
Ayita opened a bank account with $800.
Eight hundred employees of a company made a total of 400 calls.
Kele added $200 to his bank account every 2 weeks.
Maria was able to travel 400 miles in 4 days.
The statement that could be an interpretation of the graph's x-intercept or y-intercept is:
Ayita opened a bank account with $800.
The y-intercept of this line represents the initial balance in the bank account.
At a carnival, single rides cost $2 each, and all day ride passes cost $15. The total revenue for the day was $2,960. Which equation can be used to represent x, the number of single ride passes sold and y, the number of all day ride passes sold?
2x + 15y = 2,960
12x + 5y = 2,960
15x + 2y = 2,960
17x + 15y = 2,960
The equation that can be used to represent x, the number of single ride passes sold and y, the number of all day ride passes sold is:
2x + 15y = 2,960
This equation expresses that the total revenue ($2,960) came from the sales of either single ride passes ($2 each) or all day ride passes ($15 each).
Based on the equation 6x + 2y = 30, what is the missing value in the table?
x
y
?
0
3
5
15
30
To find the missing value that corresponds with x = 5, we need to substitute x = 5 into the equation and solve for y:
6x + 2y = 30
6(5) + 2y = 30
30 + 2y = 30
2y = 0
y = 0
Therefore, the missing value in the table is 0.
The completed table would be:
x
y
0
0
3
15
5
0
15
0
30
0
What is the y-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
(–2, 0)
(–1, 2)
(0, 4)
(4, 0)
The y-intercept is the point where the line crosses the y-axis, meaning the x-coordinate is 0. Looking at the given points, we can see that the y-coordinate is 0 when the x-coordinate is -2 and also when the x-coordinate is 4. This means that the line is parallel to the x-axis and does not intersect the y-axis.
Therefore, the y-intercept of the graph is 0 (the line does not intersect the y-axis).
What is the x-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (0, 2) and (3, 0).
(–3, 4)
(0, 2)
(2, 0)
(3, 0)
The x-intercept is the point where the line crosses the x-axis, meaning the y-coordinate is 0. To find the x-intercept, we can substitute y = 0 into the equation of the line and solve for x:
First, we find the slope of the line using the two points:
slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 0) = -2/3
Next, we use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
y - 2 = (-2/3)(x - 0)
y = (-2/3)x + 2
Finally, we substitute y = 0 and solve for x (the x-intercept):
0 = (-2/3)x + 2
(2/3)x = 2
x = 3
Therefore, the x-intercept of the graph is (3, 0). Answer: (3, 0)
What is the y-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (0, 2) and (3, 0).
(–3, 4)
(0, 2)
(2, 0)
(3, 0)
The y-intercept is the point where the line crosses the y-axis, meaning the x-coordinate is 0. To find the y-intercept, we can substitute x = 0 into the equation of the line and solve for y:
First, we find the slope of the line using the two points:
slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 0) = -2/3
Next, we use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
y - 2 = (-2/3)(x - 0)
y = (-2/3)x + 2
Finally, we substitute x = 0 and solve for y (the y-intercept):
y = (-2/3)(0) + 2
y = 2
Therefore, the y-intercept of the graph is (0, 2). Answer: (0, 2)
The equation 12x + 15y = 390 represents the total revenue during a one-day fundraiser. In the equation, x represents the number of youth T-shirts sold, and y represents the number of adult T-shirts sold. If there were 10 youth T-shirts sold, how many adult T-shirts were sold?
18 T-shirts
20 T-shirts
24 T-shirts
45 T-shirts
We can solve for y, the number of adult T-shirts sold, if we know the value of x, the number of youth T-shirts sold. If there were 10 youth T-shirts sold, we can substitute x = 10 into the equation and solve for y:
12x + 15y = 390
12(10) + 15y = 390
120 + 15y = 390
15y = 270
y = 18
Therefore, if there were 10 youth T-shirts sold, 18 adult T-shirts were sold. Answer: 18 T-shirts.
Which is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
To graph the linear equation x - 2y = 6, we can rearrange it into slope-intercept form (y = mx + b) by solving for y:
x - 2y = 6
-2y = -x + 6
y = (1/2)x - 3
This gives us a slope of 1/2 (the coefficient of x) and a y-intercept of -3 (the constant term).
Using this information, we can eliminate options 1, 2, and 3, because they don't have a slope of 1/2 and/or don't have a y-intercept of -3.
This leaves us with option 4: On a coordinate plane, a line goes through points (0, 3) and (6, 0).
We can confirm that this is the correct graph by finding its slope and y-intercept:
slope = (y2 - y1) / (x2 - x1) = (0 - 3) / (6 - 0) = -1/2
y-intercept = 3
These values match the slope and y-intercept we found earlier, so option 4 is the correct graph. Answer: On a coordinate plane, a line goes through points (0, 3) and (6, 0).
thats incorrect there negative numbers notpositive
I apologize for the error in my previous response.
To graph the linear equation x - 2y = 6 with negative coordinates, we can again rearrange it into slope-intercept form by solving for y:
x - 2y = 6
-2y = -x + 6
y = (1/2)x - 3
This gives us a slope of 1/2 and a y-intercept of -3.
Using this information, we can eliminate options 1 and 3, because they have a y-intercept of 0 instead of -3.
This leaves us with two options: option 2 (On a coordinate plane, a line goes through points (0, -3) and (6, 0)) and option 4 (On a coordinate plane, a line goes through points (0, 3) and (6, 0)).
We can confirm the correct option by looking at the slope. Since the slope of the line is positive (1/2), the graph must rise from left to right. Therefore, the only option consistent with this requirement is option 2, in which the line passes through points with negative y-coordinates.
So the correct graph is: On a coordinate plane, a line goes through points (0, -3) and (6, 0). Answer: option 2.
Which expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction
We can use the slope formula to determine the slope of the line that passes through the points (-7, 3) and (1, -9):
slope = (y2 - y1) / (x2 - x1)
Substituting the given coordinates, we get:
slope = (-9 - 3) / (1 - (-7))
slope = (-12) / 8
slope = -3/2
Therefore, the expression that represents the slope of the line is:
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction
which simplifies to:
StartFraction -6 Over -6 EndFraction
and further simplifies to:
-3/2.
So the answer is StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction, which is equivalent to -3/2. Answer: StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction.
Which expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFractionWhich expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
StartFraction 1 minus (negative 7) Over negative 9 minus 3 EndFraction
StartFraction 1 + (negative 7) Over negative 9 + 3 EndFraction
StartFraction negative 9 minus 3 Over 1 minus (negative 7) EndFraction
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction
The correct expression to determine the slope of the line that passes through the points (-7, 3) and (1, -9) is:
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction
This expression represents the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the given coordinates, we get:
slope = (-9 - 3) / (1 - (-7))
slope = (-12) / 8
slope = -3/2
Therefore, the expression that represents the slope of the line is:
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction
which simplifies to:
StartFraction -6 Over -6 EndFraction
and further simplifies to:
-3/2.
So the answer is StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction, which is equivalent to -3/2. Answer: StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction.
A teacher presented students with four tables.
Table 1
A 2-column table with 3 rows titled Table 1. Column 1 is labeled x with entries 2, 6, 8. Column 2 is labeled y with entries 1, negative 1, negative 2.
Table 2
A 2-column table with 3 rows titled Table 2. Column 1 is labeled x with entries 0, 2, 6. Column 2 is labeled y with entries 8, 4, negative 4.
Table 3
A 2-column table with 3 rows titled Table 3. Column 1 is labeled x with entries negative 4, negative 2, 2. Column 2 is labeled y with entries 4, 5, 7.
Table 4
A 2-column table with 3 rows titled Table 4. Column 1 is labeled x with entries negative 2, 0, 4. Column 2 is labeled y with entries 0, 4, 12.
Which table describes a linear function that has a slope of 2?
Table 1
Table 2
Table 3
Table 4