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3 years ago

Find the equation of a line that passes through the point (-5,4) and is perpendicular to 6x-36y

Mathematics

1 answer:

____ [38]3 years ago

6 0

<u>Answer:</u>

$y = - 6x - 2$

<u>Explanation</u>

The given line is

$6x - 36y = k$

where k is the missing constant from the given equation( this has no effect on the solution in anyway)

We solve for y to get;

$y = \frac{1}{6}x - \frac{k}{36}$

The slope of this line after comparing to

y=mx+c is

$m = \frac{1}{6}$

The negative reciprocal is m=-6

The equation of the required line that passes through (-5,4) is given by

$y - 4 = - 6(x - - 5)$

We multiply through by 6 to get:

$y - 4 = - 6x - 30$

We expand to get;

$y = - 6x - 26$

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What is the equation of this graphed line?

barxatty [35]

Answer:

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

Step-by-step explanation:

Given:

The two points on the line are:

$(x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)$

Now, for a line with two points on it, the slope of the line is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

For the points $(x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7)$ , slope is:

$m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-7+3}{6+6}\\m=\frac{-4}{12}=-\frac{1}{3}$

Now, for a line with slope 'm' and a point $(x_1,y_1)$ on it is given as:

$y-y_1=m(x-x_1)$

Plug in all the values and determine the equation of the line. This gives,

$y-(-3)=-\frac{1}{3}(x-(-6))\\\\y+3=-\frac{1}{3}(x+6)\\\\y+3=-\frac{1}{3}x-\frac{1}{3}\times 6\\\\y+3=-\frac{1}{3}x-2\\\\y=-\frac{1}{3}x-2-3\\\\y=-\frac{1}{3}x-5$

Therefore, the equation of the line is:

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

4 0

3 years ago

In 2008 election there was 28 blue states and 22 red states express the red and blue states as fractions in lowest terms of the

Basile [38]

Let's start with the blue states. Out of 50 states, 28 of them were blue.
Therefore, the fraction would be 28/50. Let's reduce it.
28/50=14/25 --> these are the lowest terms for this fraction
Use a calculator to find the decimal solution --> 14/25= .56

Now, let's do the red states. Out of the 50 states, 22 of them were blue.
22/50=11/25 --> lowest terms
Use a calculator --> 11/25= .43

8 0

4 years ago

Simplify: 6v+v+1 learned at beggining of year btw

Readme [11.4K]

Answer:

7v +1

Step-by-step explanation:

6v+v+1

Combine like terms

7v +1

5 0

4 years ago