Download Point of Intersection Worksheet Review Sheet

UNIT 6 THE LINE REVIEW
MPM 1D5
1, Determine a rule for each table of values.
a)
b)
c)
d)
x
y
x
y
x
y
x
y
0
-3
0
-4
0
8
0
0
1
1
2
-2
1
5
1
1
2
5
4
0
2
2
2
4
3
9
6
2
3
-1
3
9
2. Sketch on a Cartesian plane a line through A(5, -2) with slope
3. State the slope of each line.
y
a)
2
3
.
y
b)
x
4. You go the Grocery store to buy apples. They are
sold by weight as shown in the chart to the right.
x
Weight
(lbs)
Cost
a) Draw a graph of Cost vs. weight.
2
$ 3.28
b) Is this relation linear?
4
$ 6.56
6
$ 9.84
c) Does it make sense to join the points?
d) Determine the slope of the line. What does the slope represent?
5. State the slope and coordinates of the y-intercept for each.
2
a) y = x - 4
b) y = -3x
c) 3x - 5y = 7
d) y = -3
5
e) 2x + 3y - 6 = 0
6 Write the equation of each line:
a) slope 5 and y-intercept 3
b) slope of -2 and passing through A(0, 4)
c)
7 On a Cartesian plane sketch the lines.
a) y =
1
x +4
3
b) y = -2
c) x = 3
8 The equation of a line is y = -2x + b. Find the value of ‘b’ if the line passes through the point
A(1, 5).
9. The equation of a line is y = mx - 5. Find the value of ‘m’ if the line passes through the point
A(2, 11).
10.A shipment of TI-83 calculators is placed in an empty shipping box. The mass of the box is
1500 g. Each calculator weighs 25 g.
a) Write an equation to show the total mass ‘m’ as the number of calculators ‘n’ increases.
b) What is the slope? What does the slope represent?
c) What is the m-intercept? What is its meaning?
11.A plane flying from Toronto to London flies at 575 km/h.
a) Write an equation to show the distance ‘d’ flown from Toronto as the time ‘t’ increases.
b) What is the slope?
c) What is the d-intercept?
12. Solve the following system by graphing:
(find the point of intersection)
y = 3x - 3
x+ y=5
13. Express in standard form:
14. Express in slope - intercept form:
b) y 
a) y = 5 - 11x
3
x 5
4
a) 2x + y - 6 = 0
b) 3x - 5y + 10 = 0
15. Find the intercepts of each line:
a) 2x – 3y – 12 = 0
b) x – 2y + 4 = 0
c) y – 3 = 0
d) y =
3
x–3
4
16. Find the equation of each line: (answers in standard form)
2
a) with slope  , passing through A(-1, 2). b) through K(2, 5) and L(-1, 3).
3
c) with slope 3 and y-intercept 2.
d) with y-intercept 3 and parallel to x + 4y - 2 = 0.
e) with x-intercept -2 and perpendicular
4
to y = x  1.
3
g) with same x-intercept as 2x - 5y = 10
and perpendicular to x - 2y - 6 = 0.
f) with same x-intercept as 3x - 2y = 6 and the
same y-intercept as y = 2x - 1.
h) parallel to the y-axis through A(1, -3).
i) parallel to the x-axis through A(-2, 4).
17. Verify that (4, -1) is the point of intersection to the system
3x + y - 11 = 0
x - 2y - 6 = 0
y
1. a) y = 4x – 3 b) y = x – 4 c) y = -3x + 8 d) y = x2
Grocery Store Apples
4.
(6, 9.84)
Cost
(4, 6.56)
(2, 3.28)
Weight
2.
3. a)
x
2
5. a)
; (0, -4) b) –3; (0, 0)
5
3
7
c)
; (0,
) d) 0; (0, -3)
5
5
2
e)
; (0, 2)
3
6. a) y = 5x + 3 b) y = -2x + 4 c) y =
2
x 1
3
1
2
b)
2
5
(5, -2)
y
y
4
7. a)
b)
x
x
y
-2
7. c)
3
x
8. b = 7 9. m = 8
10. a) m = 25n + 1500 b) 25 g/calculator c) (0, 1500)
weight of box.
11. a) d = 575t b) 575 km/h speed c) (0, 0) initial distance 12. (2, 3)
13. a) 11x + y – 5 = 0
15. a) (6,0) (0,4)
b) 3x – 4y + 20 = 0
b) (-4,0) (0,2)
14. a) y = -2x + 6
c) none (0,3)
d) (4,0) (0,-3)
b) y 
3
x2
5
16. a) 2x + 3y – 4 = 0
f) x – 2y – 2 = 0
b) 2x – 3y + 11 = 0
g) 2x + y – 10 = 0
c) 3x – y + 2 = 0
h) x – 1 = 0
d) x + 4y – 12 = 0 e) 3x + 4y + 6 = 0
i) y – 4 = 0
17. yes