Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

The required equation of a line parallel to the line will be y = 3x - 7

The required equation of the perpendicular line is y = -1/3 - 7

Using the coordinate points to get the equation of the line (1, -4) and (2, -1)

The standard form of the equation is expressed as y = mx + b

m is the slope

b is the y-intercept

Get the slope:

m = y2-y1/x2-x1

m = -1+4/2-1

m = 3/1

m = 3

Get the y-intercept

-4 = 3(1) + b

b = -4-3

b = -7

The required equation of a line parallel to the line will be y = 3x - 7

For the equation of the line perpendicular, the slope of the line will be -1/3

The required equation of the perpendicular line is y = -1/3 - 7

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(a). y = 3x - 11 ; (b). y = x - 1

Step-by-step explanation:

Parallel lines have the same slopes

Slopes of perpendicular lines are opposite reciprocals.

(3, - 2)

The slope of given line is 3

(a). Equation of ║ line is

y + 2 = 3(x - 3)

y = 3x - 11

(b). Slope of perpendicular line is

y + 2 = (x - 3)

y = x - 1

b.an increase in a causes b to decrease