Math Problem Statement

Use the slope-intercept form to graph the equation y = 4x - 4.

Solution

The problem in the image asks to graph the equation y=4x4y = 4x - 4 using the slope-intercept form.

The slope-intercept form of a linear equation is:

y=mx+by = mx + b

Where:

  • mm is the slope of the line
  • bb is the y-intercept, the point where the line crosses the y-axis

For the given equation y=4x4y = 4x - 4:

  • The slope m=4m = 4
  • The y-intercept b=4b = -4

Steps to graph the equation:

  1. Plot the y-intercept: Start by plotting the point (0,4)(0, -4) on the graph, since b=4b = -4.
  2. Use the slope: The slope m=4m = 4 means that for every 1 unit you move to the right (positive x direction), the line rises 4 units (positive y direction). Starting from (0,4)(0, -4), move 1 unit right and 4 units up to get another point (1,0)(1, 0).
  3. Draw the line: Connect the points (0,4)(0, -4) and (1,0)(1, 0), and extend the line in both directions.

Would you like to see more details or clarify anything about this?

Here are 5 related questions to explore further:

  1. How do you graph a line when the slope is negative?
  2. What happens if the y-intercept is 0?
  3. How can you determine the x-intercept from this equation?
  4. How does changing the slope affect the steepness of the line?
  5. How would you rewrite the equation if the slope and y-intercept were fractions?

Tip: To quickly find the slope from any linear equation, ensure it's in slope-intercept form y=mx+by = mx + b, where mm is always the coefficient of xx.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form: y = mx + b

Theorems

Properties of Linear Equations
Graphing Linear Equations

Suitable Grade Level

Grades 8-10