Math Problem Statement
solve
Find the x-intercept and the y-intercept of the equation 4x - 2y = 8. Then use them to graph the line.
Solution
Let's solve the equation step by step.
The given equation:
Step 1: Find the x-intercept.
At the x-intercept, . Substitute into the equation: So, the x-intercept is:
Step 2: Find the y-intercept.
At the y-intercept, . Substitute into the equation: So, the y-intercept is:
Step 3: Plot the points and draw the line.
- Plot the x-intercept at .
- Plot the y-intercept at .
- Connect these two points with a straight line.
Final Results:
- x-intercept:
- y-intercept:
Would you like a graph or further explanation? Let me know!
Here are some related questions to expand your understanding:
- How do you find intercepts in a general linear equation?
- Can we express in slope-intercept form ()?
- What is the slope of this line?
- What happens to the intercepts if the equation changes slightly, e.g., ?
- How do parallel and perpendicular lines relate to this equation?
Tip: Always verify your intercepts by substituting back into the original equation!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Intercepts
Graphing
Formulas
x-intercept: Set y = 0 in ax + by = c
y-intercept: Set x = 0 in ax + by = c
Theorems
Intercept Definition
Linear Equation Properties
Suitable Grade Level
Grades 8-10