Math Problem Statement

What is this equation in slope intercept form

What is this equation in slope-intercept form?

Solution

The equation given in the image is:

xy=3x - y = 3

To rewrite this equation in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept, follow these steps:

Steps:

  1. Start with the given equation: xy=3x - y = 3

  2. Subtract xx from both sides to isolate y-y: y=x+3-y = -x + 3

  3. Multiply through by 1-1 to make yy positive: y=x3y = x - 3

Final Answer:

y=x3y = x - 3

This is the slope-intercept form. Here:

  • The slope (mm) is 11.
  • The y-intercept (bb) is 3-3.

Do you have any questions or want further details? Here are related follow-up questions:

  1. How do you find the slope and y-intercept directly from an equation in slope-intercept form?
  2. What does the slope of m=1m = 1 mean for the graph of this equation?
  3. How would the graph of this equation look like? (E.g., the line passes through (0,3)(0, -3).)
  4. How can you convert other forms of equations (e.g., standard form) into slope-intercept form?
  5. What are some practical uses of slope-intercept form in real-life problems?

Tip:

Always isolate yy on one side of the equation to convert into slope-intercept form!

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope-Intercept Form
Linear Equations

Formulas

y = mx + b

Theorems

Properties of Linear Equations

Suitable Grade Level

Grades 7-9