6.7 Review

Leanne Thompson

6.7 Review

Find the length of each line segment formed by the points provided.

a) C (–3, 5) and D (7, 5)

b) B (–6, 6) and A (–6, –2)

c) G (–6, 4) and H (–2, 1)
An isosceles triangle has vertices P (3, 2), Q (3, 10), and R (8, 6). Draw the triangle on the grid below. Find the area and perimeter of the shape.
Find the slope of each of the following linear relations.

a)
b)

c)

d)
Graph a line with the given slope and point.

a) (–3, 3), $m=2$

b) (–3, 4), $m=-\dfrac{3}{2}$
A hiking trail rises 700 metres for every 1 000 metres of horizontal distance. What is the slope of the trail?
Use the slope formula to find the slope of the line that passes through the following points.

a) (8, 5) and (6, 3)

b) (0, 3) and (4, 6)

c) (–1, –2) and (2, 5)

d) (–25, 18) and (86, –15)
Find the unknown value in each question.

a) (0, –8) and (6, y), $m=2$

b) (x, 5) and (5, 1), $m=\dfrac{-4}{3}$

c) (–4, y) and (0, 3), $m=1$

d) (2, 4) and (x, 10), $m=\dfrac{2}{3}$
The slope of a road can be determined by measuring the change in elevation compared to the horizontal distance. If the road rises $y$ feet in height for every 48 feet of horizontal distance and the slope of the road is $\dfrac{2}{5}$ , what is the value of $y$ ? Round to the nearest tenth.
Consider the following relations.
i) Write the slope of a line that would be parallel to the given relation.
ii) Write the slope of a line that would be perpendicular to the given relation.

a)
b)

c) (–2, 5) and (7, –1)

d) (3, 9) and (1, 7)
Find the unknown value in each question using the information provided.

a) Line ST and line UV are parallel. Line ST passes through the points (–4, 3) and (n,–1), and m_ST = $-\dfrac{5}{6}$

b) Line GH and line JK are perpendicular. Line GH passes through the points (3, n) and (8, –4), and m_JK = $-2$
Find the unknown value in each question using the information provided.

a) Given that two parallel lines have the slopes $\dfrac{n}{6}$ and $-\dfrac{2}{3}$ , what is the value of n?

b) Given that two perpendicular lines have the slopes $\dfrac{5}{8}$ and $\dfrac{n}{2}$ , what is the value of n?
Write an equation in slope y-intercept form to represent the following graphs.

a)
b)
c)
Graph the following equations using the slope and y-intercept of the graph.

a) $y=\frac{2}{3}x-4$

b) $-4y-8x=-16$

c) $\frac{3}{4}x=y-2$
Identify whether the following sets of lines are parallel, perpendicular, or neither.

a) $5x+4y=1$ and $4x+5y=3$

b) $y=-\dfrac{1}{2}x-1$ and $x+2y=2$

c) $y=-3x+2$ and $x-3y=4$

d) $y=8$ and $y=-6$
Write the equation of each line in slope y-intercept form.

a) slope –7 and y-intercept (0, –1)

b) slope $m=\dfrac{5}{6}$ and containing the point (6, 3)

c) slope $m=-\dfrac{3}{4}$ and containing the point (4, –7)

d) a horizontal line containing the point (–1, 4)

e) a line containing the points (1, 4) and (6, 2)

f) a line containing the points (–4, –3) and (1, –5)

g) parallel to the line $y=\dfrac{1}{2}x-3$ and containing the point (6, 4)

h) perpendicular to the line $y=\dfrac{1}{2}x-3$ and containing the point (6, 4)

Answers

1.

a) 10

b) 8

c) 5

2. P = 20.8 units and A = 20 units²

3.

a) 1

b) $-\dfrac{3}{4}$

c) $\dfrac{2}{5}$

d) $-\dfrac{5}{2}$

4.

a)

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 3) and (negative 2, 5).

b)

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 4) and (negative 1, 1).

5. $\dfrac{7}{10}$

6.

a) 1

b) $\dfrac{3}{4}$

c) $\dfrac{7}{3}$

d) $-\dfrac{1}{3}$

7.

a) 4

b) 2

c) –1

d) 11

8. 19.2 feet

9.

a) m_parallel = $\dfrac{2}{5}$ m_{perpendicular} = $-\dfrac{5}{2}$	b) m_parallel = $-\dfrac{5}{2}$ m_{perpendicular} = $\dfrac{2}{5}$
c) m_parallel = $-\dfrac{2}{3}$ m_{perpendicular} = $\dfrac{3}{2}$	d) m_parallel = 1 m_{perpendicular} = –1

10.

a) n = $\dfrac{4}{5}$

b) n = $-\dfrac{13}{2}$

11.

a) n = –4

b) n = $-\dfrac{16}{5}$

12.

a) $y=-\dfrac{3}{2}x-1$

b) $y=\dfrac{3}{5}x+1$

c) $y=\dfrac{4}{3}x-5$

13.

a) m = $\dfrac{2}{3}$
y-int = –4
The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).

b) m = –2
y-int = 4
The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).

c) m = $\dfrac{3}{4}$
y-int = 2
The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).

14.

a) neither

b) parallel

c) perpendicular

d) parallel

15.

a) $y=-7x-1$	b) $y=\dfrac{5}{6}x-2$	c) $y=-\dfrac{3}{4}x-4$	d) $y=4$
e) $y=-\dfrac{2}{5}x+\dfrac{22}{5}$	f) $y=-\dfrac{2}{5}x-\dfrac{23}{5}$	g) $y=\dfrac{1}{2}x+1$	h) $y=-2x+16$