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2 years ago

write an equation for the line passing through the point (3,5) and perpendicular to the line y=-1/3x+5

Mathematics

1 answer:

jarptica [38.1K]2 years ago

4 0

Answer:

y= 3x -4

Step-by-step explanation:

The equation of a line can be written in the form of y=mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.

$y = - \frac{1}{3} x + 5$

Since the given equation is in the slope-intercept form, we can identify its slope from the coefficient of x.

Slope= -⅓

The product of the slopes of perpendicular lines is -1.

Slope of perpendicular line

$= - 1 \div ( - \frac{1}{3} )$

$= - 1 \times ( - \frac{3}{1} )$

= 3

Thus, the equation of the perpendicular line is given by:

y= 3x +c

Substitute a pair of coordinates that the line passes through to find the value of c.

When x= 3, y= 5,

5= 3(3) +c

5= 9 +c

<em>Minus 9 on both sides:</em>

c= 5 -9

c= -4

Hence, the equation of the perpendicular line is y= 3x -4.

Additional:

For more questions on equation of perpendicular lines, do check out the following!

brainly.com/question/2141803

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Answer:

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3 years ago

DO IT ASAP! Thank you very much!

frozen [14]

Answer:

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Step-by-step explanation:

According to the factor theorem, if x + 2 is a factor, then by dividing the polynomial by the binomial, we are meant not to have a remainder

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2 years ago

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Answer:

Step-by-step explanation:

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3 years ago

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2 years ago

Solve with interval notation Solve: 5 | x − 2 | + 4 > 8

Gnesinka [82]

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

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$\mathrm{Divide\:both\:sides\:by\:}5$

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$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

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