What is the slope perpendicular to the line y = (2/3)x + 9

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Michael H. answered • 11/11/19

High School Math, Physics, Computer Science & SAT/GRE/AP/PRAXIS Prep

Perpendicular lines have slopes whose product is -1. The slope given in

y = 3x - 2

is -3.

The slope of the perpendicular line will be m, and m needs to satisfy the equation

3 * m = -1

Hence m = -1/3.

Our perpendicular line is thus

y = (-1/3)x + b

for some constant b.

We are told that the perpendicular line goes through the point (-9,5). If so, then the following must hold:

5 = (-1/3)(-9) + b

= 3 + b

b = 2

Ans: y = (-1/3)x + 2

The key to understand this problem is that perpendicular lines have slopes that are the negative reciprocals of each other. Example, a line with slope 3/4 has a perpendicular with a slope of -4/3. So flip it over and take the negative. Like 7/12 and -12/7 or 2 and -1/2 (because 2 = 2/1)

The slope of y = 3x - 2 is 3 (the number preceding the "x' if the line is in the form y = mx + b)

So the line perpendicular to y = 3x - 2 has a slope of -1/3.

So now you just need to write the equation of the line with slope -1/3 that goes through (-9, 5). Use the point-slope form, y - y1 = m(x - x1) where (x1, y1) is (-9, 5) and m = -1/3

y - 5 = -1/3(x - -9)

y - 5 = -1/3(x + 9)

That's the answer. If they want you to give the answer in the y= mx + b format (slope-intercept) then multiply it out and combine like terms.

y - 5 = -1/3(x + 9)

y - 5 = -1/3x - 3

y = -1/3x + 2

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#y=2/7x" is in this form"#

#"with slope m "=2/7" and "b=0#

#"given the equation of a line with slope m then the "#
#"equation of a line perpendicular to it is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#rArrm_("perpendicular")=-1/(2/7)=-7/2#

#rArry=-7/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-2,9)" into the partial equation"#

#9=7+brArrb=9-7=2#

#rArry=-7/2x+2larrcolor(red)"perpendicular equation"#

The general equation of a stright line is #y=mx+n#

where m is the slope and n is y-intercept

We know also that if m is the slope, then #-1/m# is the slope of perpendicular line to the line given. In our case, we have

#m=2/7#, and #n=0# then the slope of perpendicular is #m'=-7/2#

The reuqested equation is #y=-7/2x+n#

We dont know what is the n value, but they asking for a line perpendicular passing thru #(-2,9)#, Then this point acomplish the line equation. That means #9=-7/2·(-2)+n#

Transposing terms we found #n=2#. Finally the equation is

#y=-7/2x+2#
See graph below (A is the given point)

Slope of the line perpendicular to #y# is #-3/2#
See a solution process below:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(2/3)x - color(blue)(6)#

Therefore, the slope of the line represented by the equation in the problem is:

#color(red)(m = 2/3)#

Let's call the slope of a perpendicular line: #m_p#

The slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

#m_p = -1/(2/3) = -3/2#

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What is the slope of a line perpendicular to 10x + 4y = 20?

Correct answer:

Explanation:

First, you should put the equation in slope intercept form (y = mx + b), where m is the slope.  

10x + 4y = 20

Isolate the y term

10x + 4y – 10x = 20 – 10x

4y = 20 – 10x

Rearrange the terms

4y = –10x + 20

Divide both sides by 4

The slope of the given line is –10/4. A perpendicular line will have a slope with the opposite reciprocal. In simpler terms, you flip the slope and change the sign, therefore, the opposite reciprocal is 4/10.

Find the slope of the line that is perpendicular to the line that contains (1, 9) and (3, 4).

Explanation:

The slope of the line that contains the points (1, 9) and (3, 4) is .

The negative reciprocal is , which is the slope of the perpendicular line.

If the slope of a line is equal to , what is the slope of its perpendicular intercept?

Correct answer:

Explanation:

Slope of lines that are perpendicular to each other are the negative reciprocal.

Two lines are perpendicular to each other. One of the lines is depicted by the equation . What is the slope of the other line?

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative reciprocals of one another. Since the original line has a slope of , the perpendicular line must have a slope of .

Two lines are perpendicular to each other. One of the lines' equations is .

What is the slope of the other line?

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative reciprocals of one another. The given line's slope is 5, which means that the slope of the other line must be its negative reciprocal. The negative reciprocal of 5 is .

What is the slope of a line that is perpendicular to

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative inverses of one another. The slope of the given line is . The negative inverse of is , which must be the slope of the perpendicular line.

What is the slope of a line that is perpendicular to

?

Correct answer:

Explanation:

The slopes of perpendicular lines are negative inverses of each other. The slope of the given line is . The negative inverse of is .

Find the slope of a line that's perpendicular to the following linear equation:

Correct answer:

Explanation:

We are given

To find the slope that's perpendicular, we perform the following steps

1. First, take the slope from our original equation.  In our equation, the slope is
2. Take the reciprocal of that slope.  The reciprocal is .
3. Finally, change the sign so that we end up with .  This is the number that represents the slope of the perpendicular line.

Another way to think of this problem is that the general formula for the slope that's perpendicular is

where  is the slope of the original equation.  In our case, . Thus,

A line passes through points (–6,9) and (4,–4). Find the slope of the line that runs perpendicular to this line.

Correct answer:

Explanation:

To find the slope of this perpendicular line, we need to first find the slope of the line that passes through points (–6,9) and (4,–4). Remember, the general formula for slope is , where the two points are  and .  In our case, we can calculate the slope using out two points.

The slope of the line passing through (–6,9) and (4,–4) is –13/10. To find the slope of the line that is perpendicular, just switch the sign and take the reciprocal of –13/10. This gives us 10/13. So 10/13 is the slope of that perpendicular line.

Find the slope of the line perpendicular to the line that fits the following points:

(3,5), (2,7), (0,11)

Correct answer:

Explanation:

1) To find the slope of the perpendicular line, we must first find the slope of the line fitting the given points. Slope is equal to change in  over change in .

2) The perpendicular slope is the opposite reciprocal of the slope of the line to which it is perpendicular. So flip the original slope upside down and multiply by .

Perpendicular slope

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