Math Problem Statement

Graph the problem

Graph the following features: Slope = 2, Y-intercept = 3.

Solution

The task requires graphing a line with the following properties:

  • Slope = 2
  • Y-intercept = 3

The general equation for a line in slope-intercept form is: y=mx+by = mx + b where mm is the slope and bb is the y-intercept.

Given:

  • m=2m = 2 (slope)
  • b=3b = 3 (y-intercept)

The equation of the line would be: y=2x+3y = 2x + 3

In the graph you uploaded, it seems there is a misunderstanding in the line's plot. The correct graph should:

  1. Pass through the y-intercept at (0,3)(0, 3).
  2. Have a slope of 2, which means for every unit increase in xx, yy should increase by 2 units. So, moving from (0,3)(0, 3), the next point could be (1,5)(1, 5) (since y=2(1)+3=5y = 2(1) + 3 = 5).

Let me know if you'd like a corrected graph drawn out, or if you have questions about the process!


Here are 5 related questions for further learning:

  1. How can you find the slope if given two points on a line?
  2. What changes in the equation of a line when the slope is negative?
  3. How do you determine the x-intercept from a line equation?
  4. How does the graph of a line change if you increase the y-intercept?
  5. What is the difference between slope-intercept form and point-slope form?

Tip: When graphing, always check if the line passes through the correct y-intercept and follows the slope!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope of a Line

Suitable Grade Level

Grades 8-10