Question

write the linear equation that gives the rule for the table with x values 5, 6, 7, 8 and corresponding y values -47, -50, -53, -56. write your answer as an equation with y first.

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((5, -47)\) and \((6, -50)\):
\( m=\frac{-50 - (-47)}{6 - 5}=\frac{-50 + 47}{1}=\frac{-3}{1}=-3 \)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((5, -47)\) and \( m=-3 \):
\( y-(-47)=-3(x - 5) \)
\( y + 47=-3x+15 \)
Subtract 47 from both sides:
\( y=-3x + 15-47 \)
\( y=-3x-32 \)

Answer:

\( y=-3x - 32 \)