Math Problem Statement

Consider the equation y = 15 – 5x.

Which of the following is a graph of this equation?

Solution

To determine which graph represents the equation y=155xy = 15 - 5x, let's break it down:

This equation is in slope-intercept form y=mx+by = mx + b, where:

  • mm is the slope of the line.
  • bb is the y-intercept.

For the given equation y=155xy = 15 - 5x:

  • The slope m=5m = -5, which means the line slopes downward (it decreases) as xx increases.
  • The y-intercept b=15b = 15, which means the line crosses the y-axis at y=15y = 15.

Key Features of the Graph:

  1. Y-intercept: The graph will cross the y-axis at (0,15)(0, 15).
  2. Slope: For every increase of 1 in xx, yy decreases by 5 units (since the slope is negative).

With this information, you can now identify the correct graph by:

  • Looking for a line that crosses the y-axis at y=15y = 15.
  • Ensuring the line has a downward slope, indicating that as xx increases, yy decreases.

If you can share the graph options, I can help you identify the correct one.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graphing of Linear Functions

Formulas

y = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9