Math Problem Statement
Solution
To determine which equation best describes the graph, let’s analyze the given line:
-
Identify the slope:
The line moves upwards as you move to the right, which indicates a positive slope. Therefore, the slope is positive, which eliminates options A, B, and C, because their slopes are negative. -
Y-intercept:
The line crosses the y-axis at -4. This means the y-intercept (b) is -4. -
Equation of the line:
The standard form of a linear equation is:
where is the slope and is the y-intercept.
Since the slope is positive and the y-intercept is -4, the equation becomes:
Correct Answer: D.
Let me know if you would like a breakdown of how to calculate slope or additional details!
Here are 5 related questions for practice:
- How do you calculate the slope of a line given two points?
- What is the slope-intercept form of a linear equation?
- How do you determine the y-intercept from a graph?
- How can you tell if a slope is positive or negative just by looking at the graph?
- How do you graph a line given its equation?
Tip: A positive slope means the line rises as you move to the right, while a negative slope means it falls.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing Lines
Formulas
Slope-intercept form: y = mx + b
Theorems
Slope-Intercept Properties
Suitable Grade Level
Grades 8-10