Question

Which coordinate pair fits the set of coordinates {(0, 4), (-2, 1), (-4, -2)} defined by a linearfunction?A. (5, 12)B. (6, -4)C. (-3, -1)D. (-6, -5)

Answer 1

• Take two points
• (0,4)
• (-2,1)

Slope:-

`\\ \tt\hookrightarrow m=(1-4)/(-2)=(-3)/(-2)=(3)/(2)`

Equation of line in point slope form

`\\ \tt\hookrightarrow y-4=3/2(x)`

`\\ \tt\hookrightarrow y=3/2x+4`

Check out option D

• -6,-5

`\\ \tt\hookrightarrow -5=3/2(-6)+4`

`\\ \tt\hookrightarrow -5=-9+4`

`\\ \tt\hookrightarrow -5=-5`

Hence option D is correct

Answer 2

D (-6, -5)

Explanation:

We need to create a linear function for the set of coordinates, input the x-values of the possible options into the function, then see which one gives the correct y-value.

Pick 2 coordinate pairs from the set:

Let
`(x_1,y_1)` = (0, 4)

Let
`(x_2,y_2)` = (-2, 1)

Use slope formula:
`m=(y_2-y_1)/(x_2-x_1)=(1-4)/(-2-0)=\frac32`

Use equation of a line in point-slope form to create the linear function:

`y-y_1=m(x-x_1)`

`\implies y-4=\frac32(x-0)`

`\implies y=\frac32x+4`

Therefore, the linear function is
`f(x)=\frac32x+4`

Inputting the x-values of the possible options, (-6, -5) is the only coordinate pair that is correct:

`f(-6)=\frac32(-6)+4=-5`