Math Problem Statement

Find the y-intercept of the line y = -15/8x + 9. Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

Solution

The equation given in the image is y=158x+9y = -\frac{15}{8}x + 9. This is in the slope-intercept form, which is written as:

y=mx+by = mx + b

where:

  • mm is the slope of the line, and
  • bb is the y-intercept.

In this case, b=9b = 9, so the y-intercept is 9.

Since the problem asks for the y-intercept as an integer or fraction, the answer is:

9\boxed{9}

Would you like further details on this topic or have any additional questions?

Here are 5 follow-up questions related to this problem:

  1. How do you determine the slope of a line from an equation?
  2. What is the meaning of the y-intercept in a real-world context?
  3. Can a line have a fractional y-intercept, and if so, how would it be interpreted?
  4. What happens to the y-intercept if the equation is rearranged in a different form?
  5. How do you find the x-intercept of a line from its equation?

Tip: The y-intercept is always the value of yy when x=0x = 0. In slope-intercept form, it's the constant term!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Y-Intercept
Slope-Intercept Form

Formulas

y = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9