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
Table 4
Which equation represents the linear function that is shown on the graph below?
On a coordinate plane, a line goes through points (4, 0), (6, 1), (8, 2), and (10, 3).
A)y = one-half x + 4
B)y = one-half x minus 2
C)y = 4 x minus 2
D)y = negative 2 x + 4
B) y = one-half x minus 2
Two points defining a linear function are shown in the table below.
x
y
–14
–18
–10
–12
What is the slope of the function?
Two-thirds
Three-halves
2
6
The slope of the function is 3/2 or one and a half.
What is the y-intercept of the linear equation x minus one-half y = negative 6?
The y-intercept of the linear equation x - 1/2y = -6 is found by letting x = 0 and solving for y:
0 - 1/2y = -6
Multiplying both sides by -2 gives:
y = 12
Therefore, the y-intercept of the linear equation x - 1/2y = -6 is 12.
Sanjay said that if a line has a slope of zero, then it never touches the x-axis. Which line proves that his statement is incorrect?
x = 0
y = 0
x = 1
y = 1
x = 0
The Shake Shack sells large and small shakes. A large shake costs $5, and a small shake costs $3. On Sunday, the Shake Shack had a total revenue of $479. Which equation can be used to represent x, the number of small shakes sold and y, the number of large shakes sold?
479x + 479y = 15
4x + 4y = 479
5x + 3y = 479
3x + 5y = 479
Let's use the given information to set up an equation.
Let x be the number of small shakes sold and y be the number of large shakes sold.
The cost of x small shakes is 3x dollars.
The cost of y large shakes is 5y dollars.
The total revenue is 479 dollars.
So, we can write the equation:
3x + 5y = 479
Therefore, the correct equation is:
5x + 3y = 479 is not correct.
The correct equation is 3x + 5y = 479.
Maricella plots two ordered pairs on the grid below.
On a coordinate plane, points are at (6, 2) and (8, 6).
The line segment is extended to cross both axes. What is the location of the y-intercept on the line?
(0, –22)
(0, –10)
(0, –5)
(0, 5)
We can use the two given points (6, 2) and (8, 6) to find the equation of the line that passes through them by finding the slope and then using the point-slope or slope-intercept form of the equation of a line.
First, we find the slope:
slope = (6 - 2) / (8 - 6) = 4 / 2 = 2
Next, we use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
Using the point (6, 2), we get:
y - 2 = 2(x - 6)
Simplifying and rearranging, we get:
y = 2x - 10
Therefore, the y-intercept of the line is (0, -10).
So, the answer is (0, –10).
Based on the equation 3x + 8y = 48, what is the missing value in the table?
x
y
0
?
6
11
16
48
We can use the given equation 3x + 8y = 48 to find the missing value of y when x = 0.
Substituting x = 0, we get:
3(0) + 8y = 48
Simplifying, we get:
8y = 48
Dividing both sides by 8, we get:
y = 6
Therefore, the missing value in the table is 6.
x
y
0
6
6
11
16
48
Which situation could best be represented by this linear equation?
2.75x + 3.25y = 215
Popcorn is 50 cents less expensive than pretzels. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The sales total was $215.
Pretzels cost 75 cents more than popcorn bags. The variable x represents the number of popcorn bags sold and y represents the number of pretzels sold. The sales total was $215.
There were 50 more popcorn bags sold than pretzels. The variable x represents the number of popcorn bags sold and y represents the number of pretzels sold. The sales total was $215.
Pretzels cost 50 cents less than popcorn bags. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The sales t
Pretzels cost 75 cents more than popcorn bags. The variable x represents the number of popcorn bags sold and y represents the number of pretzels sold. The sales total was $215.
A toy airplane climbs 30 vertical feet while traveling 50 feet horizontally. A toy helicopter climbs 20 feet while traveling 40 feet horizontally. Assuming a steady rate of change, which toy traveled at a greater slope?
The airplane did, because Three-fifths greater-than one-half.
The airplane did, because Five-thirds greater-than 2.
The helicopter did, because 2 greater-than five-thirds.
The helicopter did, because One-half greater-than three-fifths.
To compare the slopes of the airplane and the helicopter, we need to calculate the ratio of the vertical change (rise) to the horizontal change (run) for each toy:
- For the airplane: rise/run = 30/50 = 3/5 = 0.6
- For the helicopter: rise/run = 20/40 = 1/2 = 0.5
Since 0.6 is greater than 0.5, the airplane traveled at a greater slope than the helicopter.
Therefore, the answer is: The airplane did, because Three-fifths greater-than one-half.
A line passes through the points (9, 30) and (18, 30). Which statement is true about the line?
It has a slope of zero because the change in the y-values is 0.
It has no slope because the change in the y-values is 0.
It has a slope of zero because the change in the x-values is 0.
It has no slope because the change in the x-values is 0.
It has a slope of zero because the change in the y-values is 0.
The graph shown below represents a ladder leaning against a wall. The bottom of the ladder is 4 feet from the wall, and the top of the ladder reaches 20 feet above the ground.
A graph titled Ladder Leaning Against Wall has Feet from Wall on the x-axis and Feet above Ground on the y-axis. A line goes through points (0, 20) and (4, 0).
What is the slope of the graph?
–24
–20
–5
–4
We can use the two given points (0, 20) and (4, 0) to find the slope of the line that represents the ladder leaning against the wall.
The slope of a line is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the two points, we get:
slope = (0 - 20) / (4 - 0) = -20 / 4 = -5
Therefore, the slope of the graph is -5.
The linear equation when b = 5 and m = –2 is
y = 5x – 2.
y = 5x + 2.
y = –2x – 5.
y = –2x + 5.
When b = 5 and m = -2, the linear equation can be written as:
y = mx + b
Substituting m = -2 and b = 5, we get:
y = -2x + 5
Therefore, the correct equation is y = -2x + 5.
Based on the graph of the line below, which describes the relationship between the value of the y-intercept and the value of the slope?
On a coordinate plane, a line goes through points (0, 3) and (3, 4).
The y-intercept is 3, and the slope is One-third.
The y-intercept is One-third, and the slope is 3.
The y-intercept is 3, and the slope is 3.
The y-intercept is One-third, and the slope is One-third.
The y-intercept is 3, and the slope is One-third.
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 formula for slope which is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points that the line passes through.
Using the points (-7, 3) and (1, -9), we get:
slope = (-9 - 3) / (1 - (-7)) = (-12) / 8 = -3/2
Therefore, the correct expression for the slope is:
StartFraction negative 9 + 3 Over 1 + (negative 7) EndFraction.
A restaurant has two appetizer specials. Tomato bread costs $5.50, and stuffed mushrooms cost $6.75. The total amount in sales from the two appetizers on a Friday night was $186.75. Which equation can be used to represent x, the number of stuffed mushroom orders and y, the number of tomato bread orders?
5.5x + 6.75y = 186.75
6.5x + 5.75y = 186.75
6.5x + 5.5y = 186.75
6.75x + 5.5y = 186.75
Let's use the given information to set up an equation.
Let x be the number of stuffed mushroom orders and y be the number of tomato bread orders.
The cost of x stuffed mushrooms is 6.75x dollars.
The cost of y tomato bread is 5.50y dollars.
The total amount in sales is $186.75.
So, we can write the equation:
6.75x + 5.50y = 186.75
Therefore, the correct equation is:
6.75x + 5.50y = 186.75.
The graph below represents the total shipping cost of x items for four different companies.
Shipping Charges
A graph has number of items on the x-axis and shipping cost in dollars on the y-axis. Line W goes through points (0, 5) and (2, 13). Line U goes through (0, 12) and (3, 16). Line Y goes through (0, 10) and (2, 12). Line Z goes through (0, 0) and (2, 4).
Which list places the companies in order from the steepest slope to the least steep slope?
W, Z, U, Y
U, Y, W, Z
W, Z, Y, U
U, Y, Z, W
We can determine the slope of each line to compare their steepness.
Slope of W = (13 - 5) / (2 - 0) = 8/2 = 4
Slope of Z = (4 - 0) / (2 - 0) = 4/2 = 2
Slope of U = (16 - 12) / (3 - 0) = 4/3
Slope of Y = (12 - 10) / (2 - 0) = 2/2 = 1
So, the correct answer is: W, Z, U, Y, placing the companies in order from the steepest slope to the least steep slope.
Jalen is computing the slope of the line on the graph below.
On a coordinate plane, a line goes through points (negative 4, 0) and (2, 3).
Step 1: (–4, 0) and (2, 3)
Step 2: StartFraction negative 4 minus 2 Over 0 minus 3 EndFraction
Step 3: StartFraction negative 6 Over negative 3 EndFraction
Step 4: The slope is 2.
Which statement describes Jalen’s error?
Jalen computed the ratio of change in x to change in y.
Jalen used the ordered pairs in the wrong order.
Jalen made a computational error.
Jalen used an ordered pair that is not on the line.
Jalen computed the ratio of change in x to change in y but used the ordered pairs in the wrong order.
To compute the slope of the line passing through (-4, 0) and (2, 3), the order of the ordered pairs in Step 2 should be (2, 3) - (-4, 0) instead of (-4, 0) - (2, 3).
So, the correct process is:
Step 1: (–4, 0) and (2, 3)
Step 2: StartFraction 3 minus 0 Over 2 minus negative 4 EndFraction
Step 3: StartFraction 3 Over 6 EndFraction
Step 4: The slope is 1/2.
Therefore, Jalen used the ordered pairs in the wrong order.