Math Problem Statement
Solution
The question asks for equations of two parallel lines, labeled and , using the graph provided. Here is a step-by-step breakdown:
Step 1: Identify the slope ()
Parallel lines have the same slope. To find the slope of line , pick two clear points on the graph:
- Point 1:
- Point 2:
The slope () is calculated using the formula:
Thus, the slope of line is , and line also has the same slope since the lines are parallel.
Step 2: Find the y-intercepts ()
The slope-intercept form of a line is . To find , substitute the slope and one point on the line.
For line : The y-intercept is already visible on the graph, which is . The equation is:
For line : From the graph, the y-intercept of line is , so . The equation is:
Final Answer:
- Line :
- Line :
Would you like further details or explanations?
Here are some additional questions to expand your understanding:
- How do we find the slope of a line from a graph?
- What does it mean for two lines to be parallel in terms of their slopes?
- How can we verify that two given equations represent parallel lines?
- How can the slope-intercept form of a line be converted into the standard form?
- What is the significance of the y-intercept in a linear equation?
Tip: Always ensure you pick clear and accurate points from the graph when calculating the slope to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Parallel Lines
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Parallel lines theorem: Parallel lines have the same slope
Suitable Grade Level
Grades 8-10
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