Question

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?

y − 3 = ______ (x + 4)

Answer 1

a. y-3=-2(x+4)

Explanation:

did the quiz

Answer 2

Answer:
`y- 3 =-2(x + 4)`

Explanation:

The equation of a line passing through
`(x_1,y_1)` in point slope form is given by ;-

`(y-y_1)=m(x-x_1)`, where m is the slope of the line .

The slope of the line passing from (a,b) and (c,d) is given by :-

`m=(d-b)/(c-a)`

Then the slope of the line passing from (-4, -3) and (4, 1) is given by :-

`m=(1-(-3))/(4-(-4))=(1+3)/(4+4)=(4)/(8)=(1)/(2)`

The slope of perpendicular line =
`m_1=(-1)/(m)=(-1)/((1)/(2))=-2` [∵ product of slopes of two perpendicular line is -1]

Hence, the the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3) will be

`y- 3 =-2(x + 4)`