The equation y= 2x + 7 represents the North Path on a map.
a. Find the equation for a path that passes through the point (6, 3) and is parallel to the North Path.
b. Find the equation for a path that passes through the same point but is perpendicular to North Path.
we know that
the slope of the given equation is m=2
step 1
Find the equation for a path that passes through the point (6, 3) and is parallel to the North Path.
If two lines are parallel, then their slopes are equal
that means
the slope of the parallel line is m=2
Find the equation in slope intercept form
y=mx+b
we have
m=2
point (6,3)
substitute
3=2(6)+b
solve for b
3=12+b
b=-9
the equation is
y=2x-9
step 2
Find the equation for a path that passes through the same point but is perpendicular to North Path.
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is m=-1/2
Find the equation of teh line in slope intercept form
y=mx+b
we have
m=-1/2
point (6,3)
substitute
3=(-1/2)(6)+b
3=-3+b
b=6
therefore
the equation is
y=(-1/2)x+6