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 using the slope-intercept form.
The slope-intercept form of a linear equation is:
Where:
- is the slope of the line
- is the y-intercept, the point where the line crosses the y-axis
For the given equation :
- The slope
- The y-intercept
Steps to graph the equation:
- Plot the y-intercept: Start by plotting the point on the graph, since .
- Use the slope: The slope means that for every 1 unit you move to the right (positive x direction), the line rises 4 units (positive y direction). Starting from , move 1 unit right and 4 units up to get another point .
- Draw the line: Connect the points and , 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:
- How do you graph a line when the slope is negative?
- What happens if the y-intercept is 0?
- How can you determine the x-intercept from this equation?
- How does changing the slope affect the steepness of the line?
- 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 , where is always the coefficient of .
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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