Final answer:
To find the equation of a line that passes through (-3, -5) and is parallel to y = -2x + 1, we use the same slope of -2 and the given point to solve for the y-intercept b, which results in the final equation of the line y = -2x - 11.
Step-by-step explanation:
To find the equation of a line passing through (-3, -5) and parallel to the line y = −2x + 1, we first note that parallel lines have the same slope. The given line's slope is -2. Therefore, our new line will also have a slope of -2. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We can use the point (-3, -5) to solve for b.
By substituting the values into the equation y = mx + b we get:
−5 = (−2)×(−3) + b
This simplifies to −5 = 6 + b. Solving for b, we find:
−5 - 6 = b
b = −11
So the equation of our new line is y = −2x − 11.