a To find the equation of line q, you need to know two points through which the line passes.
B
b What can you say about the slope of line p compared to line q?
C
c By setting the equations of the lines equal to each other, you can solve for the x-coordinate where the lines intersect.
D
d Use the Distance Formula.
A
a y=- 3x+13
B
b y=1/3x+3
C
c (3,4)
D
d About 316 yards.
Practice makes perfect
a Let's draw the diagram, labeling the coordinates for the aquarium, shopping mall, and subway.
Line q is a linear function and can therefore be written in slope-intercept form
y=mx+b,
where m is slope and b is the y-intercept. By substituting the two points into the Slope Formula we can calculate the slope.
b From the diagram, we see that line p intersects the y-axis at (0,3). This means it has a y-intercept of 3. So far, we can write the equation for line p as
y=mx+3.We also know that line p runs perpendicular to line q. This means the slope of line p is the opposite reciprocal of the slope of line q. In other words, the product of the lines slopes equals - 1.
d From the coordinate plane, we see that the segment between the meeting point and the subway has endpoints at (3,4) and (9,6). Using the Distance Formula, we can find the distance of this segment.
The distance from the meeting point to the subway is sqrt(40). By multiplying this distance by 50, we get the total distance in yards:
50* sqrt(40)≈ 316 yards.
