Transcript In the xy-plane, the points with coordinates (0,-5) and (6,-2) lie on line l.

In the xy-plane, the points with coordinates (0,-5) and (6,-2) lie on line l. Line p contains
the point with coordinates (-5,0) and is perpendicular to line l. What is the x-coordinate
of the point where lines l and p intersect?
(a)
-6
(b)
-5
(c)
-4
(d)
-3
(e)
-2
Correct Answer: E
Explanation:
It is often helpful to make a sketch for this type of question.
The slope of line l is equal to
Since -5 is the y-intercept, the equation of l is
Since line p is perpendicular to line l, the slope of p is equal to -2 (the negative
reciprocal of the slope of l ). Since line p contains the point with coordinates (-5, 0), the
equation of line p can be found by substitution.
y = mx + b
0 = (-2)(-5) + b
-10 = b
y = -2x - 10
Continued>>>
To find the x-coordinate of the point where the two lines intersect, solve the
equation
The lines intersect at the point where x = -2.
It is also possible to graph the two linear equations to determine where they intersect.
Using a graphing calculator, let
and
You can find the point of
intersection graphically in the standard viewing window, or you can examine a table of
values to find the x-value where