1)We have to make a line perpendicular to y=2x+3, passing through the point (0,0).

y=2x+3
m=solpe=2

The slope of the line perpedicular to y=2x+3 is m´
m´=-1/m
m´=-1/2

Point slope form:
y-y₀=m(x-x₀)
(0,0)
m=-1/2

y-0=-1/2(x-0)
y=-x/2

Therefore, the line perpendicular to y=2x+3 is y=-x/2.

2)The point on the line y=2x+3 tha is closest to the origin is the point of intersection of the two lines.

y=2x+3
y=-x/2

We can solve this system of equations by equalization method.
2x+3=-x/2
least common multiple=2
4x+6=-x
4x+x=-6
5x=-6
x=-6/5 (=-1.2)

y=-x/2
y=-(-6/5)/2=6/10=3/5 (=0,6)

Therefore: the point of the line y=2x+3 that is closest to the origin is:
(-1.2 , 0.6)

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2 years ago