To find the equations of Runways B and C, we first need the equation of Runway A. From the information given:
- Runway A intercepts the x-axis at -4 and y-axis at 3.
Using the intercepts, we can find the slope of Runway A. The slope \( m \) can be calculated using the formula:
\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Choosing the points (-4, 0) and (0, 3):
\[ m = \frac{3 - 0}{0 - (-4)} = \frac{3}{4} \]
So the slope of Runway A is \( \frac{3}{4} \). The equation of a line in slope-intercept form is:
\[ y = mx + b \]
Here, b is the y-intercept, which is 3 for Runway A:
\[ y = \frac{3}{4}x + 3 \]
Runway B (Parallel to Runway A)
The slope of any line parallel to Runway A will be the same, \( m = \frac{3}{4} \). Thus, the general equation for Runway B would be:
\[ y = \frac{3}{4}x + b \]
where \( b \) is some value that you can choose.
Runway C (Perpendicular to Runway A)
The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. The negative reciprocal of \( \frac{3}{4} \) is \( -\frac{4}{3} \). Therefore, the equation of Runway C could be written as:
\[ y = -\frac{4}{3}x + b \]
where \( b \) is again some value that can be chosen based on the specific point it should pass through.
Conclusion
Without specific options A, B, C, D, E, or F presented as equations, I can't choose specific answers. However, any equation with a slope of \( \frac{3}{4} \) for Runway B and a slope of \( -\frac{4}{3} \) for Runway C would be valid. If you provide those options, I can help you pick the correct ones.
1 answer