Math Problem Statement

Solve this in fully slope intercept form

Write the equation of the line in fully simplified slope-intercept form based on the graph provided.

Solution

To find the equation of the line in slope-intercept form (which is y=mx+by = mx + b), we need to determine the slope mm and the y-intercept bb from the graph.

Step 1: Identify Points on the Line

Looking at the graph, two points on the line appear to be:

  1. (12,9)(-12, 9)
  2. (0,3)(0, -3) (this is also the y-intercept).

Step 2: Calculate the Slope mm

The slope formula is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Using points (12,9)(-12, 9) and (0,3)(0, -3): m=390(12)=1212=1m = \frac{-3 - 9}{0 - (-12)} = \frac{-12}{12} = -1

Step 3: Write the Equation in Slope-Intercept Form

Since the y-intercept bb is at (0,3)(0, -3), we have b=3b = -3.

Thus, the equation of the line is: y=x3y = -x - 3

Would you like more details on each step or have any questions?


Here are 5 additional questions to explore similar concepts:

  1. How would the equation change if the line had a different slope?
  2. What happens to the graph if the y-intercept is shifted up or down?
  3. Can you determine the equation of a line parallel to this one?
  4. How can you confirm the slope if only one point and the y-intercept are given?
  5. What changes would reflect the line across the x-axis?

Tip: When finding the slope, always subtract coordinates in the same order to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Linear Equations

Formulas

Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b

Theorems

Slope-intercept theorem

Suitable Grade Level

Grades 8-10