writing linear eqautions from standard form to slope-intercept form

Question

x-9y=54

Answer 1

To convert the equation from standard form (Ax + By = C) to slope-intercept form (y = mx + b), you can follow these steps.

The given equation is:

\[ x - 9y = 54 \]

1. Isolate the variable y. To do this, first move the x term to the other side:

   \[ -9y = -x + 54 \]

2. Divide every term by -9 to solve for y:

   \[ y = \frac{1}{9}x - 6 \]

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

• m (the slope) is \(\frac{1}{9}\)
• b (the y-intercept) is \(-6\)

So, the slope-intercept form of the equation \(x - 9y = 54\) is:

\[ y = \frac{1}{9}x - 6 \]