Question

Write the point-slope form of the equation of the line described.

a. Goes through: (4, 2), parallel to x =0
b. Goes through: (1, 4), parallel to y = 7/5x + 2
c. Goes through: (1, − 5), perpendicular to −x + y = 1
d. Goes through: (1, − 2), perpendicular to − x +2y =2

Answer 1

The point-slope form of the equations of the lines described in the question are: a) x=4, b) y-4=(7/5)(x-1), c) y+5=-1(x-1), and d) y+2=-2(x-1).

Step-by-step explanation:

The point-slope form of the equation of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

a) Since the line is parallel to x = 0, it means the slope is undefined. Therefore, the equation is x = 4.

b) Since the line is parallel to y = (7/5)x + 2, it means the slope is the same as the given line, which is 7/5. Therefore, the equation is y - 4 = (7/5)(x - 1).

c) Since the line is perpendicular to -x + y = 1, we need to find the slope of the given line, which is 1. The perpendicular slope is the negative reciprocal of 1, so it is -1. Therefore, the equation is y + 5 = -1(x - 1).

d) Since the line is perpendicular to -x + 2y = 2, we need to find the slope of the given line, which is 1/2. The perpendicular slope is the negative reciprocal of 1/2, so it is -2. Therefore, the equation is y + 2 = -2(x - 1).