Question

Find the equation of the line that passes through the point (-1,4) and is parallel to the line y = -2x - 1. Graph both lines.

A) y = -2x + 2.
B) y = -2x + 5.
C) y = 2x - 5.
D) y = 2x + 5.

Answer 1

To find the equation of the line that is parallel to y = -2x - 1 and passes through the point (-1,4), we need to determine the slope of the given line and use it to find the equation of the parallel line.

Step-by-step explanation:

To find the equation of the line that is parallel to y = -2x - 1 and passes through the point (-1,4), we need to determine the slope of the given line and use that slope to find the equation of the parallel line.

The slope of the given line y = -2x - 1 is -2. Since two parallel lines have the same slope, the slope of the parallel line is also -2.

Using the point-slope form of a linear equation, we can plug in the slope (-2) and the coordinates of the given point (-1,4) to find the equation of the parallel line y = mx + b.

y = -2x + b

Substituting the values of x and y from the given point (-1,4), we get 4 = -2 * -1 + b. Solving for b, we have b = 4 - 2 = 2.

Therefore, the equation of the line that passes through the point (-1,4) and is parallel to y = -2x - 1 is y = -2x + 2.