Question

Write the standard form of the equation of each line given the slope and y-intercept:

Slope: - 3
Y-intercept = -3





Slope: -3/5
Y-intercept: -1

Answer 1

To write the standard form of the equation of a line given the slope and y-intercept, we can start with the slope-intercept form of the equation, which is:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. We can then rearrange it into standard form, which is:

\[ Ax + By = C \]

where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.

1. **For the first line:**
- Slope (m) = -3
- Y-intercept (b) = -3

Starting with the slope-intercept form:
\[ y = -3x - 3 \]

To convert to standard form, we can rearrange it:
\[ 3x + y = -3 \]

For standard form, we usually prefer \( A \) to be non-negative:
\[ 3x + y = -3 \]

This is already in standard form since \( A = 3 \), \( B = 1 \), and \( C = -3 \).

2. **For the second line:**
- Slope (m) = -3/5
- Y-intercept (b) = -1

Starting with the slope-intercept form:
\[ y = -\frac{3}{5}x - 1 \]

To eliminate the fraction, multiply every term by 5:
\[ 5y = -3x - 5 \]

Now rearranging into standard form:
\[ 3x + 5y = -5 \]

Here, this is also in standard form with \( A = 3 \), \( B = 5 \), and \( C = -5 \).

**Final Answers:**
1. For the slope -3 and y-intercept -3:
\( 3x + y = -3 \)

2. For the slope -3/5 and y-intercept -1:
\( 3x + 5y = -5 \)