Step-by-step explanation:
To find the equation of the line perpendicular to line \( g \) and passing through the point \( (1, 3) \), we need to follow these steps:
1. Determine the slope of line \( g \).
2. Find the negative reciprocal of the slope of line \( g \) to get the slope of the perpendicular line.
3. Use the point-slope form of the equation to find the equation of the perpendicular line.
4. Convert the equation to slope-intercept form.
Let's go through these steps:
1. **Determine the slope of line \( g \)**:
If the graph of line \( g \) is provided, you can find two points on the line and calculate the slope using the formula:
\[ \text{Slope} = \frac{{\text{change in } y}}{{\text{change in } x}} \]
2. **Find the negative reciprocal of the slope of line \( g \)**:
Let's say the slope of line \( g \) is \( m_g \). The slope of the perpendicular line is the negative reciprocal of \( m_g \), which means it's \( -\frac{1}{m_g} \).
3. **Use the point-slope form of the equation**:
The point-slope form of the equation is:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the given point and \( m \) is the slope of the line.
Plug in \( (x_1, y_1) = (1, 3) \) and \( m = -\frac{1}{m_g} \) to get the equation.
4. **Convert the equation to slope-intercept form**:
Rewrite the equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Solve for \( y \) to get the equation in slope-intercept form.
If you provide the slope of line \( g \) or any additional information from the graph, I can help you with the calculations.
