Ask question

Ask question

All categories

3 years ago

14

Someone please help, its for a hw assignment I have due today. What is the equation of the line through (3, 7) that is perpendic

ular to the line through points (-1, -2) and (5, 3)?

1 answer:

Brilliant_brown [7]3 years ago

7 0

The required equation is:

$y=-\frac{6}{5}x+\frac{53}{5}$

Step-by-step explanation:

Let l_1 be the line through (-1, -2) and (5, 3)

and l_2 be the line we require which passes through (3,7)

We have to find the lope of l_1 first

$m_1=\frac{y_2-y_1}{x_2-x_1}\\=\frac{3-(-2)}{5-(-1)}\\=\frac{3+2}{5+1}\\=\frac{5}{6}$

we have to find the equation of line perpendicular to l1

The product of slopes of two perpendicular lines is -1

Let m_2 be the slope of l_2

Then

$\frac{5}{6}*m_2=-1\\m_2=-\frac{6}{5}$

The general slope-intercept form is:

y=mx+b

Putting the value of slope

$y=-\frac{6}{5}x+b$

To find the value of b, we will put (3,7) in the equation

$7=-\frac{6}{5}(3)+b\\7=-\frac{18}{5}+b\\b=7+\frac{18}{5}\\b=\frac{35+18}{5}\\b=\frac{53}{5}$

Putting the values of b and m in standard slope intercept form:

$y=-\frac{6}{5}x+\frac{53}{5}$

Hence,

The required equation is:

$y=-\frac{6}{5}x+\frac{53}{5}$

Keywords: Equation of line

Learn more about equation of line at:

#LearnwithBrainly

You might be interested in

2 2/3× 1 1/3 , use an area modle to solve

Ilia_Sergeevich [38]

2 2/3=8/3 and 1 1/3=4/3. 8/3×4/3=32/9. 32/9 as a mixed number is 3 5/9.

4 0

3 years ago

The coordinates of points A and L are negative 4 and 8, respectively. What is the coordinate of the midpoint between them?

olga nikolaevna [1]

The midpoints between 4 and 8 would be 6 because 4 5 6 7 8, the middle term is 6

6 0

2 years ago

The value of U.S exports to China increased from $1480 million in 2011 to $2768 million

aliya0001 [1]

The percentage of increase was 87.027... %

<em><u>Explanation</u></em>

The value of U.S exports to China increased from $1480 million to $2768 million.

Suppose, the percentage of increase is $x\%$

So, <u>the amount of increase</u> = $x\%$ of 1480 $=1480*\frac{x}{100}=14.8x$

Thus, the equation will be......

$14.8x= 2768-1480\\ \\ 14.8x=1288\\ \\ x= \frac{1288}{14.8}=87.027....$

So, the percentage of increase was 87.027... %

7 0

3 years ago

What are the steps to solve for: 1/5(x+5)=1/4(x-3)+1

andrew11 [14]

Step 1. Simplify $\frac{1}{5} (x+5)$ to $\frac{x+5}{5}$

$\frac{x+5}{5} = \frac{1}{4} (x-3)+1$

Step 2. Simplify $\frac{x+5}{5}$ to $1+ \frac{x}{5}$

$1+ \frac{x}{5} = \frac{1}{4} (x-3)+1$

Step 3. Simplify $\frac{1}{4} (x-3)$ to $\frac{x-3}{4}$

$1+ \frac{x}{5} = \frac{x-3}{4} +1$

Step 4. Cancel $1$ on both sides

$\frac{x}{5} = \frac{x-3}{4}$

Step 5. Multiply both sides by $20$ (the LCM of $5,4$ )

$4x=5(x-3)$

Step 6. Expand

$4x=5x-15$

Step 7. Subtract $5x$ from both sides

$4x-5x=-15$

Step 8. Simplify $4x-5x$ to $-x$

$-x=-15$

Step 9. Multiply both sides by $-1$

$x=15$

Done! :) Hope this helps! :)

3 0

3 years ago

Please help me. if you can help me answer multiple questions only 3. offering 30 points for it

lubasha [3.4K]

Answer:

(-9, -5)

Step-by-step explanation:

Ok, so when you move an image to the right, you are moving along the x-axis, and when you move up, you are moving up the y-axis. So if the altered image is (x,y) and the values are (-5, -1), you reverse what has been done to the image. In this case, since we moved to the right 4 units, we know that means we added 4 to x, so we subtract 4 to get -9. And then, for the y-value, because we added 4, we do the opposite, and subtract 4 to get -5. So the pre-image should be (-9, -5)

7 0

3 years ago