Math Problem Statement

iven the equations below, identify the slope and y-intercept for each then plot each equation on a cartesian plane: y=-x+4

Solution

The graph above represents the equation y=x+4y = -x + 4. The line crosses the y-axis at the y-intercept (0, 4) and has a slope of -1, indicating that the line goes downwards from left to right.

Would you like more details on any part of this process or have any other questions?

Here are five related questions you might find interesting:

  1. How would the graph change if the slope were positive?
  2. What happens to the graph if the y-intercept is increased or decreased?
  3. Can you identify the x-intercept from the equation y=x+4y = -x + 4?
  4. How would you graph y=2x+3y = -2x + 3 using the same method?
  5. What does the slope of a line tell you about its steepness?

Tip: Understanding the slope-intercept form y=mx+by = mx + b is key to quickly graphing linear equations and identifying the slope and intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Cartesian Plane

Formulas

Slope-intercept form: y = mx + b

Theorems

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Suitable Grade Level

Grades 7-9