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. y - \square = \square(x - \square)

Explanation:

Step1: Identify the red point's coordinates

The red point is at \( (-100, -50) \) (by counting grid units: x=-100, y=-50).

Step2: Find the slope (m)

Another point on the line: when \( x = 0 \), \( y = -40 \). So slope \( m=\frac{-40 - (-50)}{0 - (-100)}=\frac{10}{100}=\frac{1}{10} \).

Step3: Use point - slope form \( y - y_1 = m(x - x_1) \)

Substitute \( (x_1,y_1)=(-100, -50) \) and \( m = \frac{1}{10} \). So \( y - (-50)=\frac{1}{10}(x - (-100)) \), which simplifies to \( y + 50=\frac{1}{10}(x + 100) \). In the given form \( y - (-50)=\frac{1}{10}(x - (-100)) \), so the blanks are - 50, \( \frac{1}{10} \), - 100.

Answer:

\( y - \boldsymbol{-50} = \boldsymbol{\frac{1}{10}}(x - \boldsymbol{-100}) \) (or filled as \( y - (-50)=\frac{1}{10}(x - (-100)) \) with the values - 50, \( \frac{1}{10} \), - 100 in the respective boxes)