Math Problem Statement

what is the slope intercept for 2x+3y = 6

Solution

To find the slope-intercept form of the equation 2x+3y=62x + 3y = 6, we need to solve for yy in terms of xx and write the equation in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

Here’s the step-by-step process:

  1. Start with the equation: 2x+3y=62x + 3y = 6

  2. Subtract 2x2x from both sides to isolate the yy term: 3y=2x+63y = -2x + 6

  3. Divide both sides by 3 to solve for yy: y=23x+2y = -\frac{2}{3}x + 2

Now the equation is in slope-intercept form y=mx+by = mx + b, where:

  • The slope (mm) is 23-\frac{2}{3}.
  • The y-intercept (bb) is 22.

Do you want more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you find the slope given two points on a line?
  2. What is the significance of the y-intercept in a linear equation?
  3. How would you convert a slope-intercept form equation back to standard form?
  4. Can you graph the equation y=23x+2y = -\frac{2}{3}x + 2?
  5. What is the effect on the graph if the slope is positive instead of negative?

Tip: When graphing a line, start by plotting the y-intercept and then use the slope to find another point on the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-Intercept Form: y = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10