Question

Helppppppp
Write equations of the line through the given point a) parallel and b) normal to the given linen
a.(5,-3), x+y=4
b.(-6,2), 5x+2y=7
c.(-3,-4), y=-2

Answer 1

Slope-Intercept form is normally helpful for problems requiring the slope.

Careful with c.

Answer 2

a.(5,-3), x+y=4 (parallel lines have same slpoe)
Since line is passing through (5,-3) and is parallel to x+y=4 i.e. y= -x+4
comparing y= -x+4 by y = mx +c we find slope m= -1
eq of line in slope point form is given as
y-y1=m(x-x1)
y-(-3)=-1(x-5)
y+3=-x+5
y= -x+5-3
y=-x+2
x+y=2 is the required eq of the line

Answer 3

b.(-6,2), 5x+2y=7
Since line is passing through (-6,2) and is normal to the line 5x+2y=7
i.e. 2y = -5x+7
y=( -5/2)x+7/2
therefore m=-5/2
slope of req line = 2/5
now proceed in the same way as above

Answer 4

@Gabysolis49