Math Problem Statement
Solution
To find the equation of this line in slope-intercept form, we need two main components:
- Slope (m)
- Y-intercept (b)
The slope-intercept form of a line is given by:
Step 1: Determine the Slope (m)
The slope is calculated as: From the graph, let's choose two points on the line for clarity:
- The point where and (the y-intercept)
- Another point, such as where and
Now, using these points:
Step 2: Determine the Y-intercept (b)
From the graph, we observe that the line crosses the y-axis at . Thus, the y-intercept is 4.
Final Equation
Substituting the values of and into the slope-intercept form:
Answer
The equation of the line in slope-intercept form is:
Would you like further clarification on any step?
Here are five related questions for deeper understanding:
- How would you calculate the equation if you were given two points not on the y-axis?
- What does a positive slope indicate about the direction of a line on a graph?
- How would the equation change if the y-intercept were negative?
- How can you verify if a given point lies on a specific line using its equation?
- What would be the equation of a line parallel to this one but passing through a different y-intercept?
Tip: To check if your slope calculation is correct, try picking different pairs of points on the line and see if you obtain the same slope.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
Slope-intercept form y = mx + b
Slope formula m = (y2 - y1) / (x2 - x1)
Theorems
Slope-intercept form theorem
Suitable Grade Level
Grades 8-10
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