Math Problem Statement

y=2x+3

Solution

The equation you provided, y=2x+3y = 2x + 3, represents a linear function. Let's analyze its key components:

1. Slope-Intercept Form

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

  • mm is the slope.
  • bb is the y-intercept.

For y=2x+3y = 2x + 3:

  • Slope (m): 22
  • Y-Intercept (b): 33

2. Characteristics of the Line

  • Slope: The slope of 2 means that for every 1 unit increase in xx, the value of yy increases by 2 units.
  • Y-Intercept: The line crosses the y-axis at the point (0,3)(0, 3).

3. Graphing the Line

To graph this equation:

  1. Start by plotting the y-intercept (0, 3) on the coordinate plane.
  2. Use the slope to find another point. Since the slope is 2, move up 2 units and 1 unit to the right from the y-intercept to get the next point, (1, 5).
  3. Draw a straight line through these points.

4. Example Points on the Line

Here are a few points that satisfy the equation:

  • x=0,y=3x = 0, y = 3 (y-intercept)
  • x=1,y=5x = 1, y = 5
  • x=1,y=1x = -1, y = 1

Would you like a graph or further details?

Related Questions

  1. How do you find the slope and y-intercept from any linear equation?
  2. What is the meaning of a negative slope?
  3. How do you convert a linear equation from slope-intercept to standard form?
  4. How does changing the slope affect the graph of a line?
  5. What are parallel and perpendicular lines?

Tip: Understanding how to interpret the slope and y-intercept helps in quickly graphing and analyzing linear equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-8