writing linear eqautions from standard form to slope-intercept form

Question

2x+3y=30

Answer 1

To convert the equation \(2x + 3y = 30\) from standard form to slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. Start with the original equation: \[ 2x + 3y = 30 \]

2. Subtract \(2x\) from both sides to isolate the \(y\) term: \[ 3y = -2x + 30 \]

3. Divide every term by \(3\) to solve for \(y\): \[ y = -\frac{2}{3}x + 10 \]

Now the equation is in slope-intercept form, where:

• The slope \(m = -\frac{2}{3}\)
• The y-intercept \(b = 10\)

So, the final answer is: \[ y = -\frac{2}{3}x + 10 \]