6x-3y=30

1 answer

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!