To find the equation of the line in standard form (Ax + By = C), we can start with the slope-intercept form of the line \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Given:
- Slope (m) = 0.5
- Point = (4, -2)
First, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Substituting the coordinates of the given point and the slope into the equation:
\[ y - (-2) = 0.5(x - 4) \]
This simplifies to:
\[ y + 2 = 0.5(x - 4) \]
Distributing the 0.5:
\[ y + 2 = 0.5x - 2 \]
Now, subtract 2 from both sides:
\[ y = 0.5x - 4 \]
Next, we need to convert this equation into standard form (Ax + By = C). We can rearrange it:
\[ -0.5x + y = -4 \]
To eliminate the decimal, multiply the entire equation by 2:
\[ -2x + 2y = -8 \]
Now, rearranging to make \( A \) positive gives us:
\[ 2x - 2y = 8 \]
Thus, the standard form of the equation for the line is:
\[ 2x - 2y = 8 \]
2 answers