Math Problem Statement

This graph represents .

the graph of 2x+y=-4

Solution

The equation given is:

2x+y=42x + y = -4

We want to express this equation in slope-intercept form (y=mx+by = mx + b), where mm is the slope and bb is the y-intercept.

Step 1: Convert to slope-intercept form

Starting with: 2x+y=42x + y = -4 Subtract 2x2x from both sides: y=2x4y = -2x - 4

Step 2: Identify slope and intercept

  • The slope mm is 2-2.
  • The y-intercept bb is 4-4, meaning the line crosses the y-axis at (0,4)(0, -4).

Step 3: Drawing the graph

  1. Start at the y-intercept (0,4)(0, -4).
  2. Use the slope m=2m = -2, which means for every 1 unit you move to the right (positive direction on the x-axis), you move 2 units down (negative direction on the y-axis).

Two points on the line are:

  • (0,4)(0, -4) from the y-intercept.
  • Moving right 1 unit: (1,6)(1, -6).

Plot these points and draw a straight line through them.

Would you like more details on how to graph it?

5 Related Questions:

  1. How do you find the x-intercept of this line?
  2. What changes if the slope is positive instead of negative?
  3. How do you graph a line given two points?
  4. How do you determine if two lines are parallel?
  5. How do you find the slope between two points?

Tip

When converting to slope-intercept form, always isolate yy for easier graphing!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form y = mx + b

Theorems

Linear Equation Theorem

Suitable Grade Level

Grades 8-10