Math Problem Statement
Find the x-intercept and y-intercept of the line -8x + 5y = 14. Write your answers as exact values. Do not write your answers as ordered pairs.
Solution
To find the x-intercept and y-intercept of the given line:
We need to follow these steps:
1. Finding the x-intercept:
The x-intercept occurs when . Substitute into the equation:
Solving for :
So, the x-intercept is .
2. Finding the y-intercept:
The y-intercept occurs when . Substitute into the equation:
Solving for :
So, the y-intercept is .
Final Answer:
- The x-intercept is .
- The y-intercept is .
Do you have any questions or would you like more details on how this was solved?
Here are some related questions to expand on this topic:
- How do we graph a line using intercepts?
- What is the slope of the line given by the equation ?
- How do you rewrite the equation in slope-intercept form?
- What are the steps to find intercepts for quadratic equations?
- How do the intercepts help in understanding the behavior of a linear function?
Tip: The x-intercept occurs where the graph crosses the x-axis, and the y-intercept occurs where the graph crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Intercepts
Formulas
To find the x-intercept, set y = 0 and solve for x.
To find the y-intercept, set x = 0 and solve for y.
Theorems
-
Suitable Grade Level
Grades 7-9