writing linear eqautions from standard form to slope-intercept form

Question

5x-6y=-18

Answer 1

To convert the linear equation from standard form (Ax + By = C) to slope-intercept form (y = mx + b), we'll follow these steps:

1. Start with the standard form equation: \[ 5x - 6y = -18 \]

2. Solve for \(y\). First, isolate the term with \(y\): \[ -6y = -5x - 18 \]

3. Next, divide every term by -6 to solve for \(y\): \[ y = \frac{5}{6}x + 3 \]

Now, the equation \(y = \frac{5}{6}x + 3\) is in slope-intercept form, where:

• The slope \(m\) is \(\frac{5}{6}\)
• The y-intercept \(b\) is \(3\)