Math Problem Statement

convert 2x+3y=5 from standard for into slope-intercept form

Solution

To convert the equation 2x+3y=52x + 3y = 5 from standard form (Ax + By = C) into slope-intercept form (y = mx + b), we need to solve for yy.

Steps to Convert:

  1. Start with the given equation: 2x+3y=52x + 3y = 5

  2. Isolate the yy-term on one side: 3y=2x+53y = -2x + 5 Subtract 2x2x from both sides.

  3. Solve for yy by dividing every term by 3: y=23x+53y = -\frac{2}{3}x + \frac{5}{3}

Slope-Intercept Form:

The slope-intercept form of the equation is: y=23x+53y = -\frac{2}{3}x + \frac{5}{3}

In this form, the slope (mm) is 23-\frac{2}{3} and the y-intercept (bb) is 53\frac{5}{3}.


Would you like more details on this, or do you have any other questions?

Here are 5 related questions that you might find interesting:

  1. How do you convert an equation from slope-intercept form to standard form?
  2. What is the slope of the line perpendicular to y=23x+53y = -\frac{2}{3}x + \frac{5}{3}?
  3. How do you find the x-intercept of the line 2x+3y=52x + 3y = 5?
  4. What is the meaning of the slope and y-intercept in the context of a real-world problem?
  5. How do you graph a line given its equation in slope-intercept form?

Tip: When converting equations, carefully isolate the variable of interest by performing inverse operations systematically.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9