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