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

y= -2x + 25

y= 2x + 24

y= 2x + 21

y = -3x + 19

Answer 1

show your work

Answer 2

The correct equation that models the relationship shown in the table is:

y = -3x + 19.

This is because the data corresponds to the equation y = -3x + 25 when you plug in the x and y values from the table.

Answer 3

To find the equation of the linear function that models the relationship shown in the table, we will first calculate the slope (m) of the line using two points from the table.

Using the points (2, 21) and (10, 5):

m = (y2 - y1) / (x2 - x1)
m = (5 - 21) / (10 - 2)
m = (-16) / 8
m = -2

Now that we have found the slope (m = -2), we can substitute the slope and one of the points (2, 21) into the point-slope form of a linear equation to find the y-intercept (b).

y - y1 = m(x - x1)
y - 21 = -2(x - 2)
y - 21 = -2x + 4
y = -2x + 25

Therefore, the equation of the linear function that models the relationship shown in the table is y = -2x + 25.