Consider the following equation.

−3x+4y−19=0
Step 1 of 3 :  Express the given equation in slope-intercept form. Simplify your answer.

To express the equation \(-3x + 4y - 19 = 0\) in slope-intercept form, we need to rearrange it into the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step-by-step process:

1. Start with the original equation:
   \[
   -3x + 4y - 19 = 0
   \]

2. Move the term \(-3x\) to the other side:
   \[
   4y = 3x + 19
   \]

3. Divide both sides of the equation by 4 to isolate \(y\):
   \[
   y = \frac{3}{4}x + \frac{19}{4}
   \]

Now, the equation is in slope-intercept form:  
\[
y = \frac{3}{4}x + \frac{19}{4}
\]

The slope is \(\frac{3}{4}\) and the y-intercept is \(\frac{19}{4}\).

Would you like to ask more about this, or need more clarification?

Here are some questions you might explore next:
1. How can we find the x-intercept of this equation?
2. What is the significance of the slope in a linear equation?
3. How do we graph a line using the slope-intercept form?
4. How do you convert a slope-intercept form to standard form?
5. What is the relationship between the slope and parallel or perpendicular lines?

**Tip**: The slope \(\frac{3}{4}\) indicates that for every 4 units you move horizontally, the line rises by 3 units vertically.

Consider the following equation. −3x+4y−19=0. Step 1 of 3: Express the given equation in slope-intercept form. Simplify your answer.

Learn how to convert the linear equation −3x + 4y − 19 = 0 into slope-intercept form with a step-by-step solution. This guide simplifies algebraic rearrangement and explains key concepts like slope and intercepts, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation