Question

Find a formula for the function whose graph s the given curve.

The line segment joining the points \(\left( { - {\bf{5}},{\bf{10}}} \right)\) and \(\left( {{\bf{7}}, - {\bf{10}}} \right)\).

Short answer

The equation of the line is \(y = - \frac{5}{3}x + \frac{5}{3}\) for \( - 5 \le x \le 7\).

Step-by-step solution

Find the slope of the line

The slope of the line joining points \(\left( { - 5,10} \right)\) and \(\left( {7, - 10} \right)\) is calculated below:

\(\begin{aligned}m &= \frac{{ - 10 - 10}}{{7 - \left( { - 5} \right)}}\\ &= - \frac{{20}}{{12}}\\ &= - \frac{5}{3}\end{aligned}\)

Find the equation of the line joining two points

The equation of the linejoining \(\left( { - 5,10} \right)\) and \(\left( {7, - 10} \right)\) with slope \( - \frac{5}{3}\) is obtained below:

\(\begin{aligned}y - 10 &= - \frac{5}{3}\left( {x + 5} \right)\\3y - 30 &= - 5x - 25\\3y &= - 5x + 5\\y &= - \frac{5}{3}x + \frac{5}{3}\end{aligned}\)

So, the equation of the line is \(y = - \frac{5}{3}x + \frac{5}{3}\)for \( - 5 \le x \le 7\).