MPM1D Grade 9
INVESTIGATING RELATIONSHIPS REVIEW
1. Given that y varies directly as x. Find
a) Find the value of y when 𝑥 = 4 if 𝑦 = −6 when 𝑥 = 9.
b) Find the value of x when 𝑦 = −2 if 𝑦 = 12 when 𝑥 = 8.
2. For each equation
i) determine whether the relation is linear or non-linear;
ii) if the relation is linear, determine whether the relation represents
direct or partial variation.
a)
𝑦
𝑥
=
2
3
b) 2𝑥 2 + 3𝑦 − 1 = 0
c) 𝑥𝑦 = 4
d) 𝑥 =
4𝑦−3
2
e) 2𝑦 − 3 = 0
f) 𝑥 2 + 𝑦 2 = 1
3. Use first differences to determine from the table of values whether
each relation is linear or non-linear.
4. For the relation 𝑦 = √𝑥 − 2
a) complete the table of values;
b) plot the points on a grid with an appropriate scale;
d) join the points with a smooth curve.
5. For each of the following graphs:
i) State the slope and the intercept of the vertical axis.
ii) Interpret the slope and the intercept.
6. The cost for new wall-to wall carpeting is $250 plus $7 per square
foot.
a) Write an equation relating the cost of carpeting, C, in dollars, and the
area to be carpeted, A, in square feet.
b) How much will it cost Charlotte to carpet a room that is 250 square
feet?
c) How large a room can Charlotte afford to carpet if she has $2 500
available for the job? State your answer correct to the nearest square
foot.
7. For the pattern shown below
a) Construct a table showing at each step how many Xs are required.
Step #
Number of Xs
b) Write an equation relating the step number, n, with the number of Xs
required, x.
c) How many Xs would there be in the 99𝑡ℎ step?
8. Ira uses a GPS to track his progress on a hike over gently rolling
terrain. Periodically he checks the GPS and notes how much time, t, in
minutes, has passed since he began hiking and how far he has travelled,
d, in km. The table below shows the values that Ira records.
a) Graph the data.
b) Draw a line of best fit.
c) Write an equation for the line of best fit.
d) Does your equation represent direct or partial variation?
e) Assuming that Ira does not get tired, how long should it take for Ira to
hike 15 km?
9. A number of items were selected from McDonald’s menu. The table
below shows the number of calories, C, and the number of grams of fat,
f, in each item.
a) Graph the data with C as the independent variable.
b) Draw a line of best fit.
c) Find an equation for the line of best fit.
d) Does your equation represent direct or partial variation?
e) A Quarter Pounder has 410 calories. Predict the number of grams of
fat in a Quarter Pounder.
10. The table below shows Taylor’s height, h, in inches, versus her age,
a, in years.
a) Graph the data.
b) Draw the line of best fit.
c) Write an equation for the line of best fit.
d) Does your equation represent direct or partial variation?
e) What does the h-intercept of the line of best fit represent? Does this
value make sense? Explain.
f) Find the slope of your line of best fit. What does this slope represent?
g) Predict how tall Taylor will be when she is done growing at age 16.
State your answer correct to the nearest inch.
11. Recreational pilots looking for flight time must either
 rent a plane by the hour;
 buy their own plane;
 buy a plane in partnership with another pilot.
The graph below illustrates the annual cost, C, versus flight time, t, in
hours, for each of these options.
a) What do the C-intercepts of each line represent?
b) What is the hourly cost of renting?
c) What is the hourly cost of owing?
d) If Howard usually flies about 60 hours per year, what is the cheapest
option for him?
e) How many hours per year must Howard fly in order to justify owing
his plane?
12. At 9:00 a.m. on Monday morning, Chris begins a hike up a trial to a
cabin in the mountains. Sometime later, Alex, who spent the night in the
cabin, begins to hike down the same trial. The graph below shows the
distance vs. Time graph for both hikers. State speeds in km/h.
a) How far is it from where Chris begins to hike to the cabin?
b) How fast is Chris hiking when he begins his climb?
c) How fast does Alex hike down the trail?
d) At what time do Chris and Alex pass each other along the trail?
e) How fast is Chris hiking when he passes Alex?
f) How long does it take Alex to hike down from the cabin?
g) Chris stops for a rest on his climb to the cabin. What time is it when
he stops and how long does he stop for?
h) How much longer does it take Chris to hike up to the cabin than Alex
to hike down from the cabin?
i) Based on Chris’ ascent, which part of the climb is the steepest – the
beginning, the middle or the end? Explain your answer.