Question

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?

Answer 1

y = 2x - 5
y = -x + 1

2x - 5 = -x + 1
2x + x = 1 + 5
3x = 6
x = 6/3
x = 2

y = -x + 1
y = -2 + 1
y = -1

solution is (2,-1)...point of intersection between the 2 lines given.

y = 1/2x + 4....slope here is 1/2. A parallel line will have the same slope.

y = mx + b
slope(m) = 1/2
(2,-1)...x = 2 and y = -1
sub and find b
-1 = 1/2(2) + b
-1 = 1 + b
-1 -1 = b
-2 = b

so ur parallel equation is : y = 1/2x - 2 <==

Answer 2

find inersection first

both equal y so
2x-5=-x+1
3x-5=1
3x=6
x=2
sub back

y=2x-5
y=2(2)-5
y=4-5
y=-1
intersection is (2,-1)

paralell to a line is having same slope
y=mx+b, m is slope
given
y=1/2x+4
slope is 1/2
so
y=1/2x+b
find b
given the point (2,-1) that it must pass through
(x,y) so x=2 and y=-1
-1=1/2(2)+b
-1=1+b
-2=b

the equation is y=1/2x-2