Question

look at this graph: graph of a line on a coordinate plane with a red point at (-600, 400) and another point at (0, -1000) 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

From the graph, we can see two points: the red point \((-600, 400)\) and the y - intercept \((0, - 1000)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-600,400)\) and \((x_2,y_2)=(0, - 1000)\).
\(m=\frac{-1000 - 400}{0-(-600)}=\frac{-1400}{600}=-\frac{7}{3}\)

Step3: Write the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We use the point \((x_1,y_1)=(-600,400)\) and \(m =-\frac{7}{3}\).
Substitute into the formula: \(y - 400=-\frac{7}{3}(x + 600)\)

Answer:

\(y - 400=-\frac{7}{3}(x + 600)\)