Math Problem Statement

y-1=-5(x-1) Graph the equation

Solution

To graph the equation y1=5(x1)y - 1 = -5(x - 1), we need to first rewrite it into slope-intercept form (y=mx+by = mx + b).

Step 1: Expand the equation

y1=5(x1)y - 1 = -5(x - 1) Distribute the 5-5 on the right-hand side: y1=5x+5y - 1 = -5x + 5

Step 2: Solve for yy

Add 1 to both sides to isolate yy: y=5x+6y = -5x + 6

Now, the equation is in slope-intercept form: y=5x+6y = -5x + 6, where:

  • The slope (mm) is 5-5, meaning the line goes down 5 units for every 1 unit it moves to the right.
  • The y-intercept (bb) is 6, meaning the line crosses the y-axis at (0,6)(0, 6).

Step 3: Plotting the graph

  1. Start at the y-intercept: Plot the point (0,6)(0, 6).
  2. Use the slope: From (0,6)(0, 6), move 1 unit to the right and 5 units down to find another point. This gives the point (1,1)(1, 1).
  3. Draw the line: Connect the two points with a straight line, extending it in both directions.

Would you like me to generate a visual graph of this equation for you?

Related Questions:

  1. How do you calculate the slope of a line between two points?
  2. What does the slope tell you about the steepness of a line?
  3. How can you determine the x-intercept of this line?
  4. What are other forms of linear equations besides slope-intercept form?
  5. How do you graph lines parallel or perpendicular to this one?

Tip: When graphing, always check your slope and intercept points to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope of a Line
Point-Slope Form

Suitable Grade Level

Grades 8-10