To find the initial value of the linear function (the y-intercept or b), we can use the point-slope formula:
y = mx + b
Substitute m = -47, x = 14, y = 3 into the equation:
3 = (-47)(14) + b
3 = -658 + b
b = 3 + 658
b = 661
Therefore, the initial value of the linear function is b = 661.
None of the options provided match the correct answer, so the closest option would be:
D. b = 15.71
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.
A. b = 12.29
B. b = −5
C. b = 11
D. b = 15.71
5 answers
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.
A. The initial value is 2/3, and the rate of change is −2/3.
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 1/6, and the rate of change is 3/2.
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.
A. The initial value is 2/3, and the rate of change is −2/3.
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 1/6, and the rate of change is 3/2.
To find the initial value and the rate of change of the linear function represented by the upward slanting line passing through the points (-4, -10/3) and (-1, -4/3), we first need to determine the slope of the line (rate of change).
First, find the slope (m) using 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 = 2/3
So, the rate of change (slope) of the linear function is 2/3.
Next, we can find the initial value (y-intercept, b) by using the point-slope formula:
y = mx + b
-4/3 = 2/3 * -1 + b
-4/3 = -2/3 + b
b = -4/3 + 2/3
b = -2/3
Therefore, the initial value of the linear function is -2/3, and the rate of change is 2/3.
The correct answer is:
C. The initial value is −2/3, and the rate of change is 2/3.
First, find the slope (m) using 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 = 2/3
So, the rate of change (slope) of the linear function is 2/3.
Next, we can find the initial value (y-intercept, b) by using the point-slope formula:
y = mx + b
-4/3 = 2/3 * -1 + b
-4/3 = -2/3 + b
b = -4/3 + 2/3
b = -2/3
Therefore, the initial value of the linear function is -2/3, and the rate of change is 2/3.
The correct answer is:
C. The initial value is −2/3, and the rate of change is 2/3.
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.
A. The initial value is 0, and the rate of change is 1/2.
B. The initial value is 2, and the rate of change is 2.
C. The initial value is −6, and the rate of change is 2.
D. The initial value is 0, and the rate of change is 2.
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.
A. The initial value is 0, and the rate of change is 1/2.
B. The initial value is 2, and the rate of change is 2.
C. The initial value is −6, and the rate of change is 2.
D. The initial value is 0, and the rate of change is 2.
To find the initial value and the rate of change of the linear function represented by the upward slanting line passing through the points (-1.5, -3), (0, 0), and (0.5, 1), we need to first calculate the slope (rate of change).
First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1.5, -3) and (x2, y2) = (0, 0)
m = (0 - (-3)) / (0 - (-1.5))
m = 3 / 1.5
m = 2
So, the rate of change (slope) of the linear function is 2.
Next, we can find the initial value (y-intercept, b) by using the point-slope formula with one of the points (0, 0):
y = mx + b
0 = 2(0) + b
0 = 0 + b
b = 0
Therefore, the initial value of the linear function is 0, and the rate of change is 2.
The correct answer is:
D. The initial value is 0, and the rate of change is 2.
First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1.5, -3) and (x2, y2) = (0, 0)
m = (0 - (-3)) / (0 - (-1.5))
m = 3 / 1.5
m = 2
So, the rate of change (slope) of the linear function is 2.
Next, we can find the initial value (y-intercept, b) by using the point-slope formula with one of the points (0, 0):
y = mx + b
0 = 2(0) + b
0 = 0 + b
b = 0
Therefore, the initial value of the linear function is 0, and the rate of change is 2.
The correct answer is:
D. The initial value is 0, and the rate of change is 2.