Question

Write an equation of the line that passes through (-5, -2) and is parallel to (y = 2/3x + 1).

a) (y = 2/3x - 13/3)
b) (y = 3/2x - 1\)
c) (y = 2/3x - 1\)
d) (y = 2/3x - 2/3)

Answer 1

To find the equation of a line parallel to y = (2/3)x + 1 and passing through the point (-5, -2), we can use the point-slope form of a line.

Step-by-step explanation:

To find the equation of a line parallel to y = (2/3)x + 1 and passing through the point (-5, -2), we need to use the fact that parallel lines have the same slope. The given line has a slope of 2/3, so the parallel line will also have a slope of 2/3. Using the point-slope form of a line, the equation of the parallel line can be written as:

y - y1 = m(x - x1)

Substituting the coordinates of the given point and the slope, we get:

y + 2 = (2/3)(x + 5)

Simplifying this equation gives us the answer:

y = (2/3)x - 13/3