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 y=23x+5y = -\frac{2}{3}x + 5 with a yy-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 y=23x+5y = -\frac{2}{3}x + 5 is 23-\frac{2}{3}.

Step 2: Write the Equation of the New Line

  • Since we want a line that is parallel, it will have the same slope: 23-\frac{2}{3}.

  • The general equation for a line is: y=mx+by = mx + b, where:

    • mm is the slope.
    • bb is the yy-intercept.
  • For our new line, the slope m=23m = -\frac{2}{3} and yy-intercept b=2b = 2.

  • Thus, the equation of the new line is: y=23x+2y = -\frac{2}{3}x + 2

Step 3: Graph the Line

  • Plot the yy-intercept (0, 2) on the graph.
  • Use the slope 23-\frac{2}{3}:
    • 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:

  1. How do you find the slope of a line from its equation?
  2. What is the difference between parallel and perpendicular lines?
  3. How do you graph lines with positive slopes?
  4. How can you find the equation of a line given two points?
  5. 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