Math Problem Statement
Solution
To determine the equation of the line shown in the graph in slope-intercept form (), let's calculate the slope () and y-intercept ().
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Finding the slope (): The slope is the change in over the change in . Using two points on the line:
- Point 1:
- Point 2:
So, the slope is .
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Finding the y-intercept (): The y-intercept is where the line crosses the -axis. Observing the graph, the line crosses the -axis at .
Thus, the equation of the line is:
Would you like a detailed explanation of how these steps were calculated, or do you have additional questions? Here are five related questions to consider:
- How can we verify the slope by using other points on the line?
- What would the equation look like if it were expressed in standard form?
- How can the slope-intercept equation help determine other points on the line?
- What does the slope tell us about the steepness of the line?
- How do we find the equation of a line parallel or perpendicular to this one?
Tip: When determining the slope, always ensure you're using points exactly on the grid lines to avoid estimation errors.
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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
Basic properties of linear equations
Suitable Grade Level
Grades 7-9