Question

writing linear eqautions from standard form to slope-intercept form
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 \( -2 \).