Math Problem Statement
Solution
To find the equation of the line in slope-intercept form (), we need two key pieces of information:
- The slope (): This is the "rise over run," or the change in over the change in .
- The y-intercept (): This is the point where the line crosses the -axis.
Step 1: Find the slope
Looking at the graph, the line passes through the points and .
Using the slope formula: Substituting the points and : So, the slope .
Step 2: Find the y-intercept
The y-intercept is the value of when . From the graph, we can see that the line crosses the -axis at . Therefore, .
Step 3: Write the equation
Now that we have the slope and the y-intercept, the equation of the line is:
This is the equation of the line in slope-intercept form.
Would you like any further details or explanations?
Here are 5 questions that expand on this concept:
- How do you calculate the slope when given two points on a line?
- What is the meaning of the slope and y-intercept in real-world problems?
- How does the slope affect the direction of a line on a graph?
- How would the equation change if the line had a positive slope?
- Can you determine the equation of a vertical or horizontal line?
Tip: The steeper the line, the larger the absolute value of the slope!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10
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