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Mrs. Jackson gives the table below to her students.

X Y
4 26
5 23
6 M


In order for the function to be linear, what must m be and why?
m = 22 because the rate of change is 1.
m = 20 because the rate of change is 3.
m = 22 because the rate of change is –1.
m = 20 because the rate of change is –3.

Respuesta :

carlosego

For this case, the slope of the line is given by:

[tex] a=\frac{y2-y1}{x2-x1} [/tex]

Substituting values, we have:

[tex] a=\frac{23-26}{5-4} [/tex]

Rewriting:

[tex] a=\frac{-3}{1}

a = -3 [/tex]

Then, since the value of the slope is constant for a line then we can rewrite the slope equation to find the value of M.

We have then:

[tex] -3 = \frac{M-23}{6-5} [/tex]

From here, we clear the value of M:

[tex] -3 = \frac{M-23}{1}

-3 = M - 23

M = 23 - 3

M = 20 [/tex]

Answer:

m = 20 because the rate of change is –3.

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