Coordinates and linear graphs

Advanced Math 7 · Unit 10 · slope-linear-graphs · Teacher edition

slope-linear-graphs

Name ______________________________Date ______________

1.
Find the slope of the line through $(2, 5)$ and $(6, 17)$ .
Answer: ______________
2.
Write an equation of the line through $(0, 3)$ and $(4, 1)$ .
Answer: ______________
3.
The water level in a tank, in cm, after $t$ minutes of draining is given by $h = 60 - 4t$ . Which statement is correct?
1. (A)
  The tank starts at $60$ cm and the level falls $4$ cm every minute.
2. (B)
  The tank starts at $4$ cm and the level falls $60$ cm every minute.
3. (C)
  The tank starts at $60$ cm and the level rises $4$ cm every minute.
4. (D)
  The tank is empty after $4$ minutes.
4.
What is the slope of the line through $(1, 2)$ and $(4, 8)$ ?
1. (A)
  $\dfrac{1}{2}$
2. (B)
  $2$
3. (C)
  $-2$
4. (D)
  $6$
5.
The points $(-2, 11)$ , $(1, 2)$ , and $(4, k)$ lie on the same straight line. What is $k$ ?
Answer: ______________

Answer key — Coordinates and linear graphs

1.
3slope-linear-graphs-01
$m = \frac{17 - 5}{6 - 2} = \frac{12}{4} = \mathbf{3}$ .
2.
$y=-\frac{1}{2}x+3$ slope-linear-graphs-02
$c = 3$ and $m = \frac{1 - 3}{4 - 0} = -\frac{1}{2}$ , so $\mathbf{y = -\tfrac{1}{2}x + 3}$ . Check $(4, 1)$ : $-\frac{1}{2}(4) + 3 = 1$ . ✓
3.
(A)
The tank starts at $60$ cm and the level falls $4$ cm every minute.
slope-linear-graphs-03
$h = -4t + 60$ : the tank starts at $60$ cm and falls $4$ cm per minute — the first statement. (It is empty when $60 - 4t = 0$ , at $t = 15$ minutes, not $4$ .)
4.
(B)
$2$
slope-linear-graphs-04
$m = \frac{8 - 2}{4 - 1} = \frac{6}{3} = \mathbf{2}$ . ( $\frac{1}{2}$ is $\frac{\Delta x}{\Delta y}$ , upside down; $-2$ subtracts in opposite orders; $6$ is just the rise.)
5.
-7slope-linear-graphs-05
$m = \frac{2 - 11}{1 - (-2)} = \frac{-9}{3} = -3$ . From $(1, 2)$ to $(4, k)$ the run is $3$ , so the rise is $-9$ : $k = 2 - 9 = \mathbf{-7}$ . Check: $\frac{-7 - 2}{4 - 1} = -3$ . ✓