Math Problem Statement

Graph the following features: - Slope = 2 - Y-intercept = -2

Solution

The image asks for a graph of a line with the given features:

  • Slope: 2
  • Y-intercept: -2

Step-by-Step Solution:

  1. Identify the equation of the line:

    • The slope-intercept form of a line is given by: y=mx+by = mx + b where mm is the slope and bb is the y-intercept.

    • For the given features: y=2x2y = 2x - 2

  2. Plot the y-intercept:

    • The y-intercept is -2. This is the point where the line crosses the y-axis. Plot this point at (0, -2) on the graph.
  3. Use the slope to find another point:

    • The slope is 2, which can be interpreted as a rise of 2 units for every run of 1 unit.
    • From the point (0, -2), move up 2 units and to the right 1 unit. This lands on the point (1, 0).
  4. Draw the line:

    • Draw a straight line passing through the points (0, -2) and (1, 0). Extend the line in both directions.

Would you like me to generate an image of the graph or explain any other details?

Related Questions:

  1. What is the general form of the equation of a line?
  2. How do you convert a line from slope-intercept form to standard form?
  3. How does the slope of a line affect its steepness?
  4. What is the significance of the y-intercept in a graph?
  5. How can we find the x-intercept of a line given its equation?

Tip: When graphing lines, always start with the y-intercept and then use the slope to find additional points.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Slope-Intercept Form

Formulas

Slope-intercept form: y = mx + b

Theorems

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Suitable Grade Level

Grades 6-8