Question

the graph of a linear function passes through the points (-6, 26) and (9, -39). write an equation for the function. show your work.

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-6, 26)\) and \((x_2, y_2)=(9, - 39)\).
\[m=\frac{-39 - 26}{9-(-6)}=\frac{-65}{15}=-\frac{13}{3}\]

Step2: Use point - slope form to find the equation

The point - slope form of a linear equation is \(y - y_1=m(x - x_1)\). We can use the point \((-6,26)\) and \(m =-\frac{13}{3}\).
\[y - 26=-\frac{13}{3}(x + 6)\]
Expand the right - hand side:
\[y-26=-\frac{13}{3}x-26\]
Add 26 to both sides of the equation:
\[y=-\frac{13}{3}x\]

Answer:

The equation of the linear function is \(y =-\frac{13}{3}x\)