Question
Which equation of the linear function models the relationship shown in the table.
x y
2 21
4 17
5 15
8 9
10 5
(1 point)
Responses
y=−2x+25
y is equal to negative 2 x plus 25
y=2x+24
y is equal to 2 x plus 24
y=2x+21
y is equal to 2 x plus 21
y=−3x+19
x y
2 21
4 17
5 15
8 9
10 5
(1 point)
Responses
y=−2x+25
y is equal to negative 2 x plus 25
y=2x+24
y is equal to 2 x plus 24
y=2x+21
y is equal to 2 x plus 21
y=−3x+19
Answers
Answer
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Answered by
GPT 3.5
y=−2x+25
y is equal to negative 3 x plus 25
y is equal to negative 3 x plus 25
Answered by
GPT 3.5
To find the equation of the linear function that models the relationship shown in the table, we need to calculate the slope (m) and the y-intercept (b) using two points from the table.
Let's take the points (2, 21) and (4, 17) to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (17 - 21) / (4 - 2)
m = -4 / 2
m = -2
Now that we have the slope, we can use the slope-intercept form of a line (y = mx + b) to find the y-intercept (b). We can substitute one of the points into the equation:
Using point (2, 21):
21 = -2(2) + b
21 = -4 + b
b = 21 + 4
b = 25
Therefore, the linear function model is:
y = -2x + 25
So the correct equation is y = -2x + 25.
Let's take the points (2, 21) and (4, 17) to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (17 - 21) / (4 - 2)
m = -4 / 2
m = -2
Now that we have the slope, we can use the slope-intercept form of a line (y = mx + b) to find the y-intercept (b). We can substitute one of the points into the equation:
Using point (2, 21):
21 = -2(2) + b
21 = -4 + b
b = 21 + 4
b = 25
Therefore, the linear function model is:
y = -2x + 25
So the correct equation is y = -2x + 25.