9 answers
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Use the table to answer the question.
x y
2.6 −6
3.2 3
Determine the rate of change of the linear function given as a table of values.
(1 point)
Responses
A. m=0.067
B. m=−5
C. m=−15
D. m=15
Bot GPT 3.5
answered
To find the rate of change (slope) of the linear function, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the values from the table:
m = (3 - (-6)) / (3.2 - 2.6)
m = (3 + 6) / 0.6
m = 9 / 0.6
m = 15
Therefore, the rate of change of the linear function given in the table is 15.
Answer: D. m=15
Connexus Student
answered
Find the initial value of the linear function, given that the rate of change is m=−47 , and (14,3) is an (x,y) value of the linear function.(1 point)
Responses
A. b=12.29
B. b=15.71
C. b=11
D. b=−5
Bot GPT 3.5
answered
To find the initial value or y-intercept (b) of the linear function, we can use the point-slope form of a linear equation, which is:
y = mx + b
Given that the rate of change (slope) is m = -47, we can use the point (14, 3) to find the initial value:
3 = -47(14) + b
3 = -658 + b
b = 3 + 658
b = 661
Therefore, the initial value or y-intercept of the linear function is 661.
Answer: None of the provided responses is correct.
Connexus Student
answered
Find the initial value of the linear function, given that the rate of change is m=−4/7 , and (14,3) is an (x,y) value of the linear function.(1 point)
Responses
A. b=12.29
B. b=15.71
C. b=11
D. b=−5
Bot GPT 3.5
answered
To find the initial value or y-intercept (b) of the linear function, we can use the point-slope form of a linear equation, which is:
y = mx + b
Given that the rate of change (slope) is m = -4/7 and the point (14, 3) is on the line, we can substitute these values into the equation to solve for b:
3 = (-4/7)(14) + b
3 = -8 + b
b = 3 + 8
b = 11
Therefore, the initial value or y-intercept of the linear function is 11.
Answer: C. b = 11
Connexus Student
answered
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 4 comma start fraction negative 10 over 3 end fraction right parenthesis, and left parenthesis negative 1 comma start fraction negative 4 over 3 end fraction right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
Responses
A. The initial value is 1/6, and the rate of change is 3/2.
B. The initial value is −2, and the rate of change is 2/3.
C. The initial value is −2/3, and the rate of change is 2/3.
D. The initial value is 2/3, and the rate of change is −2/3.
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page 27 of 27
Bot GPT 3.5
answered
To find the initial value and the rate of change of the linear function as given in the graph, we can use the coordinates provided:
Point 1: (-4, -10/3)
Point 2: (-1, -4/3)
To find the rate of change (slope), we use the formula:
m = (y2 - y1) / (x2 - x1)
m = (-4/3 - (-10/3)) / (-1 - (-4))
m = (-4/3 + 10/3) / 3
m = 6/3 / 3
m = 2
To find the initial value or y-intercept (b), we can use one of the points and the computed slope:
Using point 1 (-4, -10/3):
-10/3 = 2(-4) + b
-10/3 = -8 + b
b = -10/3 + 8
b = 14/3
Therefore, the initial value is 14/3 and the rate of change is 2.
Answer: A. The initial value is 14/3, and the rate of change is 2.
Connexus Student
answered
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 1.5 comma negative 3 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 0.5 comma 1 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
Responses
A. The initial value is 2, and the rate of change is 2.
B. The initial value is −6, and the rate of change is 2.
C. The initial value is 0, and the rate of change is 2.
D. The initial value is 0, and the rate of change is 12.
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page 27 of 27
Bot GPT 3.5
answered
To find the initial value and the rate of change of the linear function as given in the graph, we can use the coordinates provided:
Point 1: (-1.5, -3)
Point 2: (0, 0)
Point 3: (0.5, 1)
To find the rate of change (slope), we use the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - (-3)) / (0 - (-1.5))
m = 3 / 1.5
m = 2
The rate of change is 2.
To determine the initial value, we choose one of the points (let's use (0, 0)) and use the formula:
y = mx + b
0 = 2(0) + b
0 = b
The initial value is 0.
Therefore, the initial value is 0 and the rate of change is 2.
Answer: C. The initial value is 0, and the rate of change is 2.