https://file.aiquickdraw.com/mathbot/file/1729540927443botv9cxb.jpg

We are tasked with finding the equation of a line that has a slope of \(-\frac{4}{9}\) and passes through the point \((-7, 0)\). Let's solve for both the slope-intercept form and the standard form of the line.

### 1. Slope-intercept form:
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \(m\) is the slope and \(b\) is the y-intercept. We are given:
- Slope \(m = -\frac{4}{9}\)
- The point \((-7, 0)\) lies on the line.

We can substitute the values of \(x = -7\), \(y = 0\), and \(m = -\frac{4}{9}\) into the slope-intercept equation to find \(b\):
\[
0 = -\frac{4}{9}(-7) + b
\]
\[
0 = \frac{28}{9} + b
\]
\[
b = -\frac{28}{9}
\]

So, the slope-intercept form of the equation is:
\[
y = -\frac{4}{9}x - \frac{28}{9}
\]

### 2. Standard form:
The standard form of a line is given by:
\[
Ax + By = C
\]
We can rearrange the slope-intercept form into standard form.

Starting from:
\[
y = -\frac{4}{9}x - \frac{28}{9}
\]
Multiply through by 9 to eliminate the fractions:
\[
9y = -4x - 28
\]
Now rearrange to get the standard form:
\[
4x + 9y = -28
\]

Thus, the equation in standard form is:
\[
4x + 9y = -28
\]

Would you like further details on this or clarification on any step?

### Related Questions:
1. What is the process to convert slope-intercept form into standard form?
2. How do you find the slope if given two points on a line?
3. What is the significance of the y-intercept in a line equation?
4. How would the equation change if the slope were positive?
5. How can you graph a line using its equation in slope-intercept form?

#### Tip: 
When converting from slope-intercept to standard form, always aim to clear fractions by multiplying through by the denominator!

Write an equation for the line that has slope -4/9 and goes through the point (-7, 0).

This problem guides you through writing the equation of a line with slope -4/9 passing through the point (-7, 0). Learn how to express the equation in both slope-intercept and standard forms, with step-by-step calculations. Suitable 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