Answer:
y = -2x + 21.
Explanation:
To find the equation of a line parallel to the line y = -2x + 1 and passing through the point (4, 13), we need to determine the slope (m) of the new line.
Since the line we want is parallel to y = -2x + 1, it will have the same slope. Therefore, the slope of the new line is -2.
Using the point-slope form of a line, which states y - y₁ = m(x - x₁), we can substitute the values (x₁, y₁) = (4, 13) and m = -2 into the equation:
y - 13 = -2(x - 4)
Next, we can distribute the -2 on the right side:
y - 13 = -2x + 8
Finally, rearranging the equation in slope-intercept form, we isolate y:
y = -2x + 8 + 13
Simplifying further:
y = -2x + 21
Therefore, the equation of the line parallel to y = -2x + 1 and passing through the point (4, 13) is y = -2x + 21.