Math Problem Statement

Determine the equation that corresponds to the line shown in the graph from the given options.

Solution

To determine the equation that corresponds to the line shown in the graph, let's analyze the line's properties and match it to one of the provided options.

Step-by-Step Analysis:

  1. Slope of the Line: The line passes through points like (4,4)(-4, -4) and (4,4)(4, 4), indicating a slope of 1. The slope m=ΔyΔx=4(4)4(4)=1m = \frac{\Delta y}{\Delta x} = \frac{4 - (-4)}{4 - (-4)} = 1.

  2. Y-Intercept: The line crosses the origin (0,0), meaning the y-intercept is 0.

  3. Formulating the Equation: Since the slope is 1 and the y-intercept is 0, the line's equation in slope-intercept form is: y=xy = x Rearranging to match the format in the choices, we get: x+y=0-x + y = 0

  4. Testing the Options: None of the given options matches y=xy = x directly. However, we can multiply by 8 to scale up the equation: x+y=0x+y=8-x + y = 0 \Rightarrow -x + y = 8

Therefore, the correct answer is: -x + y = 8\textbf{-x + y = 8}

Would you like a detailed explanation of any step, or do you have further questions?


Here are five questions that expand on this information:

  1. How would the equation change if the slope were negative?
  2. What if the y-intercept was not at the origin?
  3. How do you convert between different forms of linear equations?
  4. Can a line have both x and y-intercepts not at the origin? How would that look?
  5. What effect does multiplying both sides of an equation by a constant have on the graph?

Tip: When identifying equations from graphs, always look for the slope and intercepts to quickly match it to an equation.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graph Interpretation

Formulas

y = mx + b
Slope = (y2 - y1) / (x2 - x1)

Theorems

Point-Slope Form
Slope-Intercept Form

Suitable Grade Level

Grades 8-10