Math Problem Statement
Solve this in fully slope intercept form
Solution
To find the equation of the line in slope-intercept form (which is ), we need to determine the slope and the y-intercept from the graph.
Step 1: Identify Points on the Line
Looking at the graph, two points on the line appear to be:
- (this is also the y-intercept).
Step 2: Calculate the Slope
The slope formula is: Using points and :
Step 3: Write the Equation in Slope-Intercept Form
Since the y-intercept is at , we have .
Thus, the equation of the line is:
Would you like more details on each step or have any questions?
Here are 5 additional questions to explore similar concepts:
- How would the equation change if the line had a different slope?
- What happens to the graph if the y-intercept is shifted up or down?
- Can you determine the equation of a line parallel to this one?
- How can you confirm the slope if only one point and the y-intercept are given?
- What changes would reflect the line across the x-axis?
Tip: When finding the slope, always subtract coordinates in the same order to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Linear Equations
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b
Theorems
Slope-intercept theorem
Suitable Grade Level
Grades 8-10
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