Krystina is trying to derive the slope of a line with coordinates (6,−2)
and (0,8)
using the formula ΔyΔx=y2−y1x2−x1
.
Krystina says the slope is −35
because slope =riserun=x2−x1y2−y1=0−68−(−2)=−68+2=−610
.
Is Krystina’s calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect?
(1 point)
Responses
Krystina is incorrect because she calculated the change in x over the change in y.
Krystina is correct and she simplified the slope correctly.
Krystina is incorrect because she calculated the change in y over the change in x.
Krystina is correct because she calculated the change in x over the change in y.
Line A is perpendicular to line B.
In order for two lines to be perpendicular, their slopes must be negative reciprocals of each other.
The slope of Line A is 2, and the slope of Line B is also 2. Since the slopes are equal, Line A and Line B are not perpendicular.
The slope of Line C is -12, and the slope of Line D is 12. The slopes are opposite reciprocals of each other. Therefore, Line C and Line D are perpendicular.
Therefore, the correct statement is that Line C is perpendicular to Line D.
Krystina is incorrect because she calculated the change in x over the change in y. The correct calculation for slope using the given formula would be Δy/Δx = (y2 - y1)/(x2 - x1). In this case, it would be (8 - (-2))/(0 - 6), which simplifies to 10/(-6) or -5/3.
Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts.
This statement is correct. In order for two lines to be parallel, they must have the same slope. If Marco verifies that the lines have the same slope (which in this case is 23), he can then determine if they are parallel by checking if they have different y-intercepts. In this case, the y-intercepts are 7 and -5, which are different. Therefore, the lines are parallel.
Marco is trying to determine whether the following two lines are parallel.
y=23x+7
y=23x−5
Which statement correctly describes the approach Marco should take based on the best reasoning?
Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts.
Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes.
Use the table to answer the question.
Line Equation
Line A
y=2x−3
Line B
y=2x+5
Line C
y=−12x−2
Line D
y=12x+2
Given the linear equations in the table, which of the following statements is true?
(1 point)
Responses
Line C is perpendicular to line D
Line A is perpendicular to line C
Line A is perpendicular to line B
Line B is perpendicular to line D