Math Problem Statement

What is the equation shown in the image and its interpretation?

Solution

The equation in the image is:

y=2x+3y = -2x + 3

This is a linear equation in slope-intercept form, y=mx+by = mx + b, where:

  • m=2m = -2 is the slope of the line, indicating that the line decreases by 2 units for every 1 unit increase in xx.
  • b=3b = 3 is the y-intercept, meaning the line crosses the y-axis at y=3y = 3.

Would you like a detailed explanation on graphing this equation or its properties? Let me know if you have any specific questions.

Here are 5 related questions:

  1. How can you find the x-intercept of this equation?
  2. What is the slope of a perpendicular line to this one?
  3. How does changing the value of the slope affect the steepness of the line?
  4. How do you write the equation of a line that passes through a given point and is parallel to this one?
  5. How do you determine whether a point lies on this line?

Tip: In linear equations, the slope tells you how steep the line is, while the y-intercept tells you where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form y = mx + b

Theorems

Slope of a line
Y-intercept

Suitable Grade Level

Grades 7-9