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Margarita [4]
4 years ago
9

Which pair of equations represents two perpendicular lines ? Please help !!

Mathematics
1 answer:
Gennadij [26K]4 years ago
7 0

Slope-intercept form:

y = mx + b   "m" is the slope, "b" is the y-intercept


For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -3/4

perpendicular line's slope is 4/3


#1: The slopes are the same, meaning they are parallel lines


#2: First isolate the "y" in the first equation

-4x + 5y = -5

5y = -5 + 4x

y = -1 + 4/5x   They are not perpendicular because the slopes are 4/5 and -4/5


#3: Isolate "y" in the second equation

8y = 3x - 32

y = 3/8x - 4         They are perpendicular


#4: Isolate "y" is the 1st equation

10y = -9x

y = -9/10x     They are parallel lines



The 3rd choice is your answer

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I hope that you are doing well, during this weird time; and that this message finds you in a good place.

To get you started on this problem, you will want to think about how to go about graphing this linear function. You want to keep in mind that you want to plot your dependent variable on the y-axis, as it changes with respect to your independent variable (plotted on the x-axis). In this problem, the cost of the water bill depends on the amount of water used, in HCF. So the graph should be plotted with cost on the y-axis, and HCF on the x-axis.

It follows that you are given the coordinates of (16, $48.37) and (22, y2); where y2 represents the cost when using 22 HCF. You are also given the slope of your line (m, in y = mx + b format). You may recall that you can set-up a slope as the change in y over the change in x, or the "rise over the run" [m = (y2-y1) / (x2-x1)]. We can set this problem up, using this equation to solve for y2 (the cost at 22 HCF) algebraically.

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