Final answer:
To find the equation of a line parallel to y = -3x + 4 and passing through the point (-9, 4), use the slope -3 and the given point to solve for the y-intercept, resulting in the equation y = -3x - 23.
Step-by-step explanation:
The question involves finding the equation of a line that is parallel to another line and passes through a specific point. The given line is assumed to be y = -3x + 4. Since parallel lines have the same slope, the new line will also have a slope of -3. To find the y-intercept of the new line, we'll use the point (-9, 4) and the slope in the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Here's how we can find the equation:
- Start with the slope-intercept form: y = mx + b.
- Plug in the values for the slope (m = -3) and the coordinates of the given point (-9, 4): 4 = (-3)(-9) + b.
- Simplify and solve for b: 4 = 27 + b which yields b = -23.
- Write the final equation using the slope and the y-intercept: y = -3x - 23.
This equation represents the line that is parallel to the given line and passes through the point (-9, 4).