Math Problem Statement

Put the following equation of a line into slope-intercept form, simplifying all fractions. 2, y, minus, 2, x, equals, 4 2y−2x= 4

Solution

The given equation is:

2y2x=42y - 2x = 4

To put this into slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept, follow these steps:

  1. Add 2x2x to both sides to move the xx-term to the right-hand side: 2y=2x+42y = 2x + 4

  2. Divide every term by 2 to solve for yy: y=x+2y = x + 2

Thus, the equation in slope-intercept form is:

y=x+2y = x + 2

Here, the slope m=1m = 1, and the y-intercept b=2b = 2.

Would you like more details on any step?

Here are 5 questions related to this topic:

  1. How do you find the slope from an equation in slope-intercept form?
  2. What is the significance of the y-intercept in a linear equation?
  3. How would you graph this line using its slope and y-intercept?
  4. Can you convert a line from point-slope form to slope-intercept form?
  5. How do you determine if two lines are parallel using their equations?

Tip: To quickly find the slope of a line from an equation in standard form Ax+By=CAx + By = C, rearrange it to slope-intercept form and check the coefficient of xx.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form y = mx + b

Theorems

Linear Equation Transformation

Suitable Grade Level

Grades 7-9