Math Problem Statement

Write the linear equation in slope-intercept form and simplify: -25x - 5y = -15

Solution

The equation given is:

25x5y=15-25x - 5y = -15

We are asked to rewrite this equation in slope-intercept form, which is:

y=mx+by = mx + b

where mm is the slope and bb is the y-intercept. Let's work through the steps:

Step 1: Move the xx-term to the other side

We want to isolate the yy-term on the left side. Add 25x25x to both sides of the equation:

5y=25x15-5y = 25x - 15

Step 2: Solve for yy

To isolate yy, divide every term by 5-5:

y=25x5155y = \frac{25x}{-5} - \frac{15}{-5}

Simplifying the fractions:

y=5x+3y = -5x + 3

Final Answer:

The slope-intercept form of the equation is:

y=5x+3y = -5x + 3

Would you like further clarification or details?

Here are 5 related questions you might find helpful:

  1. How can you find the slope of a line from two points?
  2. What does the y-intercept represent in a real-world context?
  3. How do you graph a line using the slope-intercept form?
  4. How can you convert slope-intercept form to standard form?
  5. How can you find the equation of a line parallel to a given line?

Tip: The slope is the coefficient of xx, and it tells you how steep the line is. A negative slope means the line decreases from left to right.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Algebra

Formulas

y = mx + b

Theorems

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Suitable Grade Level

Grades 8-10