Math Problem Statement

Write the equation of the line in fully simplified slope-intercept form.

Solution

To write the equation of the line in slope-intercept form (y=mx+by = mx + b), let's analyze the given graph:

Steps to Solve:

  1. Find the slope (mm): The slope mm is calculated as: m=riserunm = \frac{\text{rise}}{\text{run}} From the graph, pick two points on the line:

    • Point 1: (4,8)(-4, 8)
    • Point 2: (4,4)(4, -4)

    Calculate the slope: m=484(4)=128=32m = \frac{-4 - 8}{4 - (-4)} = \frac{-12}{8} = -\frac{3}{2}

  2. Find the yy-intercept (bb): The yy-intercept is where the line crosses the yy-axis. From the graph, this occurs at b=6b = 6.

  3. Write the equation: Substitute m=32m = -\frac{3}{2} and b=6b = 6 into the slope-intercept form: y=32x+6y = -\frac{3}{2}x + 6

Final Equation:

y=32x+6y = -\frac{3}{2}x + 6

Let me know if you need more details or have any questions!

Related Questions:

  1. How is slope-intercept form derived, and why is it useful?
  2. How can you find the slope if only one point and the yy-intercept are known?
  3. What is the significance of a negative slope in a graph?
  4. How do you verify if a point lies on a given line?
  5. How can you rewrite this equation in standard form?

Tip: When identifying the slope from a graph, always check for the simplest points (integer coordinates) to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9