Question

look at this graph:
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.
y - (square) = (square)(x - (square))

Explanation:

Step1: Identify the red point

From the graph, the red point has coordinates \((600, -200)\) (assuming the grid and the position of the red dot: x=600, y=-200).

Step2: Find the slope of the line

We can also see that the line passes through the origin \((0,0)\) and the red point \((600, -200)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0,0)\) and \((600, -200)\):
\(m=\frac{-200 - 0}{600 - 0}=\frac{-200}{600}=-\frac{1}{3}\)

Step3: Write the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope. Using the red point \((x_1 = 600,y_1=-200)\) and \(m =-\frac{1}{3}\), we substitute these values into the formula:
\(y-(-200)=-\frac{1}{3}(x - 600)\) which simplifies to \(y + 200=-\frac{1}{3}(x - 600)\)

Answer:

\(y - (-200)=-\frac{1}{3}(x - 600)\) or filling in the boxes: \(y-(-200)=\boxed{-\frac{1}{3}}(x - \boxed{600})\) (the first box is \(- 200\), the second box is \(-\frac{1}{3}\), the third box is \(600\))