Math Problem Statement
Graph a line parallel to y=-2/3x+5 with a y intercept of2
Solution
To graph a line parallel to the given line with a -intercept of 2, we need to follow these steps:
Step 1: Understand the Properties of Parallel Lines
- Parallel lines have the same slope.
- The slope of the given line is .
Step 2: Write the Equation of the New Line
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Since we want a line that is parallel, it will have the same slope: .
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The general equation for a line is: , where:
- is the slope.
- is the -intercept.
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For our new line, the slope and -intercept .
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Thus, the equation of the new line is:
Step 3: Graph the Line
- Plot the -intercept (0, 2) on the graph.
- Use the slope :
- From the point (0, 2), move down 2 units and right 3 units to find another point.
- Mark this point and draw a line through both points.
Would you like a visual graph of this line?
Here are some related questions:
- How do you find the slope of a line from its equation?
- What is the difference between parallel and perpendicular lines?
- How do you graph lines with positive slopes?
- How can you find the equation of a line given two points?
- What happens if two lines have the same slope but different intercepts?
Tip: Parallel lines will never intersect, as their slopes are identical.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Parallel Lines
Formulas
y = mx + b (slope-intercept form)
Theorems
Parallel Line Theorem
Suitable Grade Level
Grades 8-10