Question

what is the equation of the line in standard form that passes throught hte point (3 4) and is parallel to the line y=-x+6

a) x+y=1
b) x+y=7
c) x-y=-1
d) x-y=-7

Answer 1

The answer is b.
The gradient of the line y=-x+6 is -1, thus the gradient of line through (3 ,4) is also -1.
Equation of a line is: y-y1=m(x-x1)
substitute
y1=4
m=-1
x1=3
so y-4=-1(x-3)
rearrange to give
y+x=7