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 the red point's coordinates

The red point is at (4, -5) (from the graph: x=4, y=-5).

Step2: Find the slope (m)

The line passes through (4, -5) and another point, say when x=5, y=0 (since it crosses x-axis at (5,0)). Slope \( m = \frac{0 - (-5)}{5 - 4} = \frac{5}{1} = 5 \).

Step3: Apply point - slope formula

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(4, - 5) \) and \( m = 5 \). Substitute: \( y - (-5)=5(x - 4) \), which simplifies to \( y + 5 = 5(x - 4) \).

Answer:

\( y + 5 = 5(x - 4) \)