12 multiple-choice questions, progressively harder.
What is the slope of the line through (−3,−7)(-3, -7)(−3,−7) and (−3,2)(-3, 2)(−3,2)?
Solution
Correct answer: D
Both points share x=−3x = -3x=−3, so the run is zero.
m=2−(−7)−3−(−3)=90m = \frac{2 - (-7)}{-3 - (-3)} = \frac{9}{0}m=−3−(−3)2−(−7)=09
Dividing by zero has no value, so the slope is undefined (a vertical line).
The line through (k,2)(k, 2)(k,2) and (7,10)(7, 10)(7,10) has slope 444. What is kkk?
Correct answer: C
Set the slope formula equal to 444 and solve for kkk.
10−27−k=4,87−k=4,7−k=2\frac{10 - 2}{7 - k} = 4, \qquad \frac{8}{7 - k} = 4, \qquad 7 - k = 27−k10−2=4,7−k8=4,7−k=2
So k=5k = 5k=5.
A line has slope 23\tfrac{2}{3}32 and passes through (−2,1)(-2, 1)(−2,1). Stepping along it, which point is on the line?
Correct answer: B
Read 23\tfrac{2}{3}32 as a run of 333 and a rise of 222. Step twice from (−2,1)(-2, 1)(−2,1).
(−2,1)→(1,3)→(4,5)(-2, 1) \to (1, 3) \to (4, 5)(−2,1)→(1,3)→(4,5)
So (4,5)(4, 5)(4,5) is on the line.
What is the slope of the line through (3,3)(3, 3)(3,3) and (3,−5)(3, -5)(3,−5)?
Both points share x=3x = 3x=3, so the run is zero.
m=−5−33−3=−80m = \frac{-5 - 3}{3 - 3} = \frac{-8}{0}m=3−3−5−3=0−8
What is the slope of the line through (−6,4)(-6, 4)(−6,4) and (−2,−2)(-2, -2)(−2,−2)?
Apply the slope formula and simplify.
m=−2−4−2−(−6)=−64=−32m = \frac{-2 - 4}{-2 - (-6)} = \frac{-6}{4} = -\frac{3}{2}m=−2−(−6)−2−4=4−6=−23
So the slope is −32-\tfrac{3}{2}−23.
What is the slope of the line through (−5,2)(-5, 2)(−5,2) and (5,2)(5, 2)(5,2)?
Both points share the height y=2y = 2y=2, so the rise is zero.
m=2−25−(−5)=010=0m = \frac{2 - 2}{5 - (-5)} = \frac{0}{10} = 0m=5−(−5)2−2=100=0
So the slope is 000 (a horizontal line).
Which pair of points lies on a line with slope 000?
Correct answer: A
Slope 000 needs a rise of 000, so the two points must share a yyy-coordinate.
m=3−35−2=03=0m = \frac{3 - 3}{5 - 2} = \frac{0}{3} = 0m=5−23−3=30=0
The pair (2,3)(2, 3)(2,3) and (5,3)(5, 3)(5,3) works. The pair sharing x=2x = 2x=2 is undefined, not 000.
What is the slope of the line through (−1,−1)(-1, -1)(−1,−1) and (3,7)(3, 7)(3,7)?
m=7−(−1)3−(−1)=84=2m = \frac{7 - (-1)}{3 - (-1)} = \frac{8}{4} = 2m=3−(−1)7−(−1)=48=2
So the slope is 222.
A line has slope −34-\tfrac{3}{4}−43. Between two of its points the run is 888. What is the rise?
The rise is the slope times the run.
rise=−34×8=−6\text{rise} = -\tfrac{3}{4} \times 8 = -6rise=−43×8=−6
So the rise is −6-6−6 (the line drops 666 units).
Which is steeper, the line through (1,2)(1, 2)(1,2) and (4,11)(4, 11)(4,11), or the line through (0,0)(0, 0)(0,0) and (2,4)(2, 4)(2,4)?
Find each slope and compare sizes.
m1=11−24−1=3,m2=4−02−0=2m_1 = \frac{11 - 2}{4 - 1} = 3, \qquad m_2 = \frac{4 - 0}{2 - 0} = 2m1=4−111−2=3,m2=2−04−0=2
Since 3>23 > 23>2, the first line is steeper.
The line through (−4,y)(-4, y)(−4,y) and (2,3)(2, 3)(2,3) has slope 12\tfrac{1}{2}21. What is yyy?
Set the slope formula equal to 12\tfrac{1}{2}21 and solve for yyy.
3−y2−(−4)=12,3−y6=12,3−y=3\frac{3 - y}{2 - (-4)} = \frac{1}{2}, \qquad \frac{3 - y}{6} = \frac{1}{2}, \qquad 3 - y = 32−(−4)3−y=21,63−y=21,3−y=3
So y=0y = 0y=0.
What is the slope of the line through (7,2)(7, 2)(7,2) and (1,5)(1, 5)(1,5)?
Take (7,2)(7, 2)(7,2) as point one and simplify.
m=5−21−7=3−6=−12m = \frac{5 - 2}{1 - 7} = \frac{3}{-6} = -\frac{1}{2}m=1−75−2=−63=−21
So the slope is −12-\tfrac{1}{2}−21.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.