Math Problem Statement
Use the intercepts to graph the equation x - 4y = 8.
Solution
To graph the equation using the intercepts, let's find the - and -intercepts and then plot the line through those points.
Step 1: Find the -intercept
The -intercept occurs where .
- Substitute into the equation:
- Simplify to find :
So, the -intercept is at .
Step 2: Find the -intercept
The -intercept occurs where .
- Substitute into the equation:
- Solve for :
So, the -intercept is at .
Step 3: Plot the Intercepts and Draw the Line
On the graph:
- Plot the point on the -axis.
- Plot the point on the -axis.
- Draw a straight line passing through these two points to represent the equation .
Would you like additional details on how this line is derived, or any assistance with other questions?
Here are five related questions to deepen your understanding:
- How would you rewrite the equation in slope-intercept form?
- What would the graph look like if the equation were ?
- How do you interpret the slope of the line from the equation ?
- How can you verify the intercepts algebraically?
- What would be the effect on the intercepts if the equation were ?
Tip: When finding intercepts, always set the opposite variable to zero, as intercepts are the points where the line crosses each axis.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Intercepts
Graphing
Formulas
x-intercept: Set y = 0 in the equation
y-intercept: Set x = 0 in the equation
Theorems
-
Suitable Grade Level
Grades 9-10