what is parallel to y=-3x-2 and passes through the point ( -4,-5 )

Answer 1

y = –3x –2

Compare with linear equation y=mx+b

m=-3 and b=-2

Method 1: Parallel line will have same slope m=-3 so equation will be y=-3x+b

As we know parallel line y=-3x+b passes through the point (-4,-5), we can find the value of b.

y=-3x+b

-5=-3(-4)+b

-5=12+b

-17=b

Parallel line equation is y=-3x-17

Method 2: Parallel line will have same slope m=-3 and passes through the point (-4,-5), we can use point equation of a line : point slope form.

m=-3, x1=-4 , y1=-5

y-y1=m(x-x1)

y-(-5)=-3(x-(-4))

y+5=-3(x+4)

y+5=-3x-12

y=-3x-17

Parallel line equation is in slope intercept form y=-3x-17

Answer 2

A line parallel to y = –3x –2 will also have slope of –3.

If the line passes through the point (–4,–5) then for every point on the line

(y – (–5))/(x – (–4)) = –3 which can be rewritten as (y + 5)/(x + 4) = –3

Multiply both sides by (x + 4) and you get

y + 5 = –3(x + 4) which is the equation for the line you are looking for in what is called point-slope form.

From here it should be too difficult to come up with the equation for the line in slope-intercept (y = mx +b) form.

Hope this helps.