Question

6x-3y=30

Answer 1

The equation you've provided is a linear equation in two variables, \( x \) and \( y \). To analyze or manipulate it, we can convert it into different forms such as the slope-intercept form (y = mx + b) or solve for one variable in terms of the other.

### Here’s how to put it in slope-intercept form:

1. Start with the original equation:
\[
6x - 3y = 30
\]

2. Solve for \( y \):
- First, isolate the term involving \( y \):
\[
-3y = -6x + 30
\]

- Next, divide all terms by -3 to solve for \( y \):
\[
y = 2x - 10
\]

Now it's in slope-intercept form, where the slope \( m \) is 2 and the y-intercept \( b \) is -10.

### If you want to express \( y \) in terms of \( x \):
From the slope-intercept form we already derived:
\[
y = 2x - 10
\]

### Alternatively, you can solve for \( x \) in terms of \( y \):
1. Start with the original equation:
\[
6x - 3y = 30
\]

2. Solve for \( x \):
- First, isolate the term involving \( x \):
\[
6x = 3y + 30
\]

- Next, divide all terms by 6:
\[
x = \frac{1}{2}y + 5
\]

### Summary:
- Slope-intercept form: \( y = 2x - 10 \)
- \( x \) in terms of \( y \): \( x = \frac{1}{2}y + 5 \)

Let me know if you need further assistance or if you would like to graph it or find specific points!