Math Problem Statement
What is the equation of this line?
Solution
The graph shows a straight line, so the equation will be in the form of , where:
- is the slope (rate of change of the line).
- is the y-intercept (the value of when ).
Step 1: Determine the slope ()
To calculate the slope, we can use two points on the line. From the image:
- The line passes through the point (the y-intercept).
- Another point the line passes through is approximately .
The formula for slope is: Substitute and : So, the slope .
Step 2: Determine the y-intercept ()
From the graph, the line crosses the y-axis at . Thus, the y-intercept .
Conclusion:
The equation of the line is:
Would you like further explanation or have any questions? Here are five related questions to expand on this:
- How do you find the equation of a line if you are given two points?
- What is the significance of the slope in a linear equation?
- How do parallel lines relate in terms of slope?
- How can we find the x-intercept of this line?
- How do you graph a line given its equation?
Tip: To quickly determine the slope visually, count the vertical and horizontal distance between two points on the line (rise over run).
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
y = mx + b
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10
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