Final answer:
To find the equation of a line parallel to y = -5x + 1 passing through (-3,-6), we use the same slope of -5 and plug the point into the slope-intercept form to find the y-intercept. The resulting equation is y = -5x - 21.
Step-by-step explanation:
The question asks to find the equation of a line that is parallel to a given line and passes through a specific point.
The given line is y = -5x + 1, which means its slope, m, is -5. Since parallel lines have the same slope, the line we are looking for will also have a slope of -5.
To find the y-intercept, b, we can use the point (-3, -6) and the slope -5 in the slope-intercept form y = mx + b. Plugging in the values we get:
- y = -5x + b
- -6 = -5(-3) + b
- -6 = 15 + b
- b = -6 - 15
- b = -21
So the equation of the line is y = -5x - 21.