Math Problem Statement

Find the slope and y-intercept of the equation -2x + y = 3.

Solution

To find the slope and yy-intercept of the equation 2x+y=3-2x + y = 3, let's rewrite it in the slope-intercept form, which is y=mx+cy = mx + c, where mm is the slope and cc is the yy-intercept.

Starting with: 2x+y=3-2x + y = 3

Add 2x2x to both sides to isolate yy: y=2x+3y = 2x + 3

Now, in this form, we can see that:

  • The slope m=2m = 2
  • The yy-intercept c=3c = 3

So, the correct answer is option (b): m=2,c=3m = 2, c = 3.

Would you like more details or have any questions?

Here are some related questions to consider:

  1. How do you convert an equation to slope-intercept form?
  2. What is the significance of the slope in a linear equation?
  3. How can you find the yy-intercept from different forms of linear equations?
  4. How do the slope and yy-intercept influence the graph of a line?
  5. What are some common methods to find the slope of a line given two points?

Tip: Always try to rewrite linear equations in slope-intercept form to easily identify the slope and yy-intercept.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + c

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9