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.

Explanation:

Step1: Identify the red point's coordinates

Looking at the graph, the red point is at \((-30, -70)\) (assuming the grid lines: from the origin, moving left 30 units (x = -30) and down 70 units (y = -70)). Also, the line crosses the x - axis at \((-40, 0)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-40,0)\) and \((x_2,y_2)=(-30,-70)\).

$$m=\frac{-70 - 0}{-30-(-40)}=\frac{-70}{10}=-7$$

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 \((-30,-70)\) and \(m = - 7\):

$$y-(-70)=-7(x - (-30))$$

Simplify to get \(y + 70=-7(x + 30)\)

Answer:

\(y + 70=-7(x + 30)\)