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:

8x+5y=14-8x + 5y = 14

We need to follow these steps:

1. Finding the x-intercept:

The x-intercept occurs when y=0y = 0. Substitute y=0y = 0 into the equation:

8x+5(0)=14    8x=14-8x + 5(0) = 14 \implies -8x = 14

Solving for xx:

x=148=74x = \frac{14}{-8} = -\frac{7}{4}

So, the x-intercept is x=74x = -\frac{7}{4}.

2. Finding the y-intercept:

The y-intercept occurs when x=0x = 0. Substitute x=0x = 0 into the equation:

8(0)+5y=14    5y=14-8(0) + 5y = 14 \implies 5y = 14

Solving for yy:

y=145y = \frac{14}{5}

So, the y-intercept is y=145y = \frac{14}{5}.

Final Answer:

  • The x-intercept is 74-\frac{7}{4}.
  • The y-intercept is 145\frac{14}{5}.

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:

  1. How do we graph a line using intercepts?
  2. What is the slope of the line given by the equation 8x+5y=14-8x + 5y = 14?
  3. How do you rewrite the equation in slope-intercept form?
  4. What are the steps to find intercepts for quadratic equations?
  5. 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

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Suitable Grade Level

Grades 7-9