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 , let's break it down:
This equation is in slope-intercept form , where:
- is the slope of the line.
- is the y-intercept.
For the given equation :
- The slope , which means the line slopes downward (it decreases) as increases.
- The y-intercept , which means the line crosses the y-axis at .
Key Features of the Graph:
- Y-intercept: The graph will cross the y-axis at .
- Slope: For every increase of 1 in , 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 .
- Ensuring the line has a downward slope, indicating that as increases, 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