Math Problem Statement

Rewrite the equation in Ax + By = C form. Use integers for A, B, and C. y + 4 = -3(x - 1)

Solution

Let's solve the given equation:

The equation provided is:

y+4=3(x1)y + 4 = -3(x - 1)

We need to rewrite it in the form:

Ax+By=CAx + By = C

Steps:

  1. First, distribute the 3-3 on the right-hand side:

y+4=3x+3y + 4 = -3x + 3

  1. Subtract 44 from both sides to isolate yy:

y=3x+34y = -3x + 3 - 4

y=3x1y = -3x - 1

  1. Now, move all terms to one side to get it in the form Ax+By=CAx + By = C:

3x+y=13x + y = -1

Thus, the equation in Ax+By=CAx + By = C form is:

3x+y=13x + y = -1

Where A=3A = 3, B=1B = 1, and C=1C = -1.


Would you like more details or have any questions? Here are some related questions for practice:

  1. How do you identify the slope and intercept from this equation?
  2. What is the slope of the line in the equation 3x+y=13x + y = -1?
  3. How would you graph the equation 3x+y=13x + y = -1?
  4. Can you write the equation in slope-intercept form from Ax+By=CAx + By = C?
  5. How do you convert a linear equation from point-slope form to standard form?

Tip: In standard form Ax+By=CAx + By = C, it's customary to have AA as a positive integer, and all coefficients should ideally be integers.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Standard Form

Formulas

Ax + By = C

Theorems

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Suitable Grade Level

Grades 7-9