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Mariana [72]
3 years ago
10

What is an equation of the line that passes through the point (8,-5) and is parallel

Mathematics
1 answer:
HACTEHA [7]3 years ago
6 0

Answer:

y=-5/4x+5

Step-by-step explanation:

Hi there!

We're given the line 5x+4y=24 and we want to find the line parallel to it that passes through (8,-5)

Parallel lines have the same slopes

First, we need to find the slope of 5x+4y=24.

We'll do that by converting 5x+4y=24 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b where m is the slope and b is the y intercept)

subtract 5x from both sides

4y=-5x+24

divide by 4 on both sides

y=-5/4x+6

since -5/4 is in the place where m should be, it is the slope.

So the equation of the line parallel to it will also have -5/4 as the slope

Here's the equation so far in slope-intercept form:

y=-5/4x+b

we need to find b

because the equation will pass through (8,-5), we can use it to solve for b

substitute 8 as x and -5 as y

-5=-5/4(8)+b

multiply

-5=-10+b

add 10 to both sides

5=b

substitute 5 as b into the equation

<u>y=-5/4x+5</u>

That's the equation of the line parallel to 5x+4y=24.

Hope this helps!

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1. Given points A(3, -5) and B(19, -1), find the coordinates of point C that sit 3/8 of the way along line AB, closer to A than
zaharov [31]

1. C(x, y) = (7.3, –3.9)

2. C(x, y) = (17, –1.5)

Solution:

Question 1:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction \frac{3}{8}.

Point divides segment in the ratio formula:

$C(x, y)=\left(\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n}\right)

Here, x_1=3, y_1=-5, x_2=19, y_2=-1 and m = 3, n = 8

$C(x, y)=\left(\frac{3\times19+8\times3}{3+8} , \frac{3\times(-1)+8\times(-5)}{3+8}\right)

           $=\left(\frac{57+24}{11} , \frac{-3-40}{11}\right)

           $=\left(\frac{81}{11} , \frac{-43}{11}\right)

C(x, y) = (7.3, –3.9)

Question 2:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction \frac{3}{8}.

Point divides segment in the ratio formula:

$C(x, y)=\left(\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n}\right)

Here, x_1=3, y_1=-5, x_2=19, y_2=-1 and m = 7, n = 1

$C(x, y)=\left(\frac{7\times19+1\times3}{7+1} , \frac{7\times(-1)+1\times(-5)}{7+1}\right)

           $=\left(\frac{133+3}{8} , \frac{-7-5}{8}\right)

           $=\left(\frac{136}{8} , \frac{-12}{8}\right)

C(x, y) = (17, –1.5)

8 0
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Answer:

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Step-by-step explanation:

12.4 lbs times 0.42 is 5.208 lbs

it is simple

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