Math Problem Statement
Solution
Let's analyze the linear graph in your image to write its equation in slope-intercept form , where:
- is the slope.
- is the y-intercept.
Step 1: Identify the y-intercept
The graph intersects the y-axis at , which means:
- .
Step 2: Find the slope
The slope is defined as: From the graph:
- Choose two points the line passes through: and .
- Rise:
- Run:
So, the slope is:
Step 3: Write the equation in slope-intercept form
Now that we know the slope and the y-intercept , the equation becomes:
This is the equation of the line in slope-intercept form.
Do you have further questions or need additional details?
Here are 5 follow-up questions you may find useful:
- How do you calculate the slope if only given two points?
- What happens to the equation if the slope is positive?
- How do you find the equation if the y-intercept is not given?
- Can we express this equation in standard form?
- What are other forms of linear equations besides slope-intercept?
Tip: When calculating slope, be careful with signs to avoid mistakes!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Slope formula
Suitable Grade Level
Grades 8-10
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