Is the Function Linear?

[nycmath]

Plot the ordered pairs (x, y) on the xy-plane, and use the average rate of change to determine whether the function is linear.

NOTE: If the function is linear, the slope will be constant.

[Eigenvalue]

Yes. The function is linear as the slope is constant.

Use 2 points to find the slope: [tex]\frac{47.5-37.5}{30-70}[/tex]=[tex]\frac{-10}{40}[/tex]=[tex]\frac{-1}{4}[/tex]

Use point-slope form to find the linear equation:
y-50=[tex]\frac{-1}{4}[/tex](x-20)

y-50=[tex]\frac{-1}{4}[/tex]x+5

y=[tex]\frac{-1}{4}[/tex]x+55

[nycmath]

Yes. The function is linear as the slope is constant.

Use 2 points to find the slope: [tex]\frac{47.5-37.5}{30-70}[/tex]=[tex]\frac{-10}{40}[/tex]=[tex]\frac{-1}{4}[/tex]

Use point-slope form to find the linear equation:
y-50=[tex]\frac{-1}{4}[/tex](x-20)

y-50=[tex]\frac{-1}{4}[/tex]x+5

y=[tex]\frac{-1}{4}[/tex]x+55

Very good.