Question

what is the equation of the line in point - slope form? use the red point in your equation. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through the y - intercept \((0, - 40)\) and the red point \((-70, - 30)\) (assuming the red point is at \(x=-70\), \(y = - 30\) by counting the grid squares. Let's confirm the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,-40)\) and \((x_2,y_2)=(-70,-30)\).

Step2: Calculate the slope \(m\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-30-(-40)}{-70 - 0}=\frac{-30 + 40}{-70}=\frac{10}{-70}=-\frac{1}{7}\)

Step3: Recall the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((-70,-30)\) (the red point) and \(m =-\frac{1}{7}\). Substitute \(x_1=-70\), \(y_1=-30\) and \(m =-\frac{1}{7}\) into the formula.
\(y-(-30)=-\frac{1}{7}(x - (-70))\)
Simplify the left - hand side and the right - hand side:
\(y + 30=-\frac{1}{7}(x + 70)\)

Answer:

\(y + 30=-\frac{1}{7}(x + 70)\)