writing linear eqautions from standard form to slope-intercept form

Question

x+5y=-10

Answer 1

To convert the equation from standard form \( Ax + By = C \) to slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, you'll want to solve for \( y \).

Starting with the equation:

\[ x + 5y = -10 \]

Follow these steps:

1. Isolate the term involving \( y \):

   Subtract \( x \) from both sides:

   \[ 5y = -10 - x \]

2. Rearrange the equation:

   You can rearrange the right side to make it more recognizable:

   \[ 5y = -x - 10 \]

3. Solve for \( y \):

   Divide every term by 5:

   \[ y = -\frac{1}{5}x - 2 \]

Now, the equation is in slope-intercept form:

\[ y = -\frac{1}{5}x - 2 \]

From this, you can see that the slope \( m \) is \( -\frac{1}{5} \) and the y-intercept \( b \) is \( -2 \).