Math Problem Statement

Create a problem using slope intercept form include a graph

Solution

Here's the graph of the line with the equation y=12x+2y = \frac{1}{2}x + 2. The red point marks the y-intercept at (0,2)(0, 2), and the green point marks (2,3)(2, 3), which lies on the line.

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. What is the slope of a line parallel to y=12x+2y = \frac{1}{2}x + 2?
  2. How would you find the equation of a line perpendicular to y=12x+2y = \frac{1}{2}x + 2?
  3. If the slope were negative, how would the graph change?
  4. How do you determine the x-intercept of the line y=12x+2y = \frac{1}{2}x + 2?
  5. Can you find the equation of a line that passes through (4,1)(4, -1) and has the same slope?

Tip: In slope-intercept form, the slope mm controls the steepness and direction of the line, while the y-intercept bb shows where it crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope-Intercept Form
Graphing Linear Equations

Formulas

Slope-intercept form y = mx + b

Theorems

Parallel and Perpendicular Line Theorems

Suitable Grade Level

Grades 7-10