Which coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function?
a) (5, 12)
b) (6, -4)
c) (-3, -1)
d) (-6, -5)

Hence,  the coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function is:

D)(-6, -5)

Step-by-step explanation:

We are given coordinates of the linear function as:

{(0,4),(-2,1),(-4,-2)}

We know that we can find the linear equation with the help of two points.

Consider two points:

(0,4) and (-2,1).

The equation of a line passing through two points (a,b) and (c,d) is given by:

Here we have:

(a,b)=(0,4) and (c,d)=(-2,1)

Hence, equation of line is:

Hence the line has slope 3/2 and y-intercept as 4.

Now we are asked to find out which point passes through the given linear function:

i.e. we will put x-value in the equation and check for which y-values hold true, the point will lie on the line segment.

A)

(5,12)

we will put x=5 in equation (1) and check whether y=12 or not.

when x=5.

Hence, option A is incorrect.

B)

(6,-4).

When x=6.

Hence, option B is incorrect.

C)

(-3,-1)

when x=-3

Hence, option C is incorrect.

D)

(-6,-5)

when x=-6

Hence option D is correct.

Hence, the coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linear function is:

D)(-6, -5)

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