Answer:
D (-6, -5)
Step-by-step 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 [tex](x_1,y_1)[/tex] = (0, 4)
Let [tex](x_2,y_2)[/tex] = (-2, 1)
Use slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-4}{-2-0}=\dfrac32[/tex]
Use equation of a line in point-slope form to create the linear function:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-4=\dfrac32(x-0)[/tex]
[tex]\implies y=\dfrac32x+4[/tex]
Therefore, the linear function is [tex]f(x)=\dfrac32x+4[/tex]
Inputting the x-values of the possible options, (-6, -5) is the only coordinate pair that is correct:
[tex]f(-6)=\dfrac32(-6)+4=-5[/tex]
Slope:-
[tex]\\ \tt\hookrightarrow m=\dfrac{1-4}{-2}=\dfrac{-3}{-2}=\dfrac{3}{2}[/tex]
Equation of line in point slope form
[tex]\\ \tt\hookrightarrow y-4=3/2(x)[/tex]
[tex]\\ \tt\hookrightarrow y=3/2x+4[/tex]
Check out option D
[tex]\\ \tt\hookrightarrow -5=3/2(-6)+4[/tex]
[tex]\\ \tt\hookrightarrow -5=-9+4[/tex]
[tex]\\ \tt\hookrightarrow -5=-5[/tex]
Hence option D is correct
