The slope of a line is 1/3 . What is the slope of a line perpendicular to this line?
2 answers:
Answer:
FIRST OPTION: -3
Step-by-step explanation:
By definition, if two lines are perpendicular to each other, then their slopes are negative reciprocals.
In this case you can observe that that the slope of the line is and you know that the other line is perpendicular to this line. Therefore, their slopes are negative reciprocals.
This means that:
If ,then
This matches with the first option.
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Answer:
k = ⅕
Step-by-step explanation:
The slope-intercept equation for a straight line is
y = mx + b, where
m = the slope and
b = the y-intercept
Data:
(3,4) = a point on the line
(3k,0) = x-intercept
(0,-5k) = y-intercept
Calculations:
1. Slope
m = (y₂ - y₁)/(x₂ - x₁) = (-5k - 0)/(0 - 3k) = -5/(-3) = ⁵/₃
This makes the equation
y = ⁵/₃x - 5k
2. k
Insert the value of the known point: (3,4)
4 = (⁵/₃)(3) - 5k
4 = 5 - 5k
-1 = -5k
k = ⅕
The figure below shows your graph passing through (3,4) with intercepts 3k and -5k on the x- and y-axes respectively .
