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Write a linear equation in standard form for the line that goes through

(-14,-5) and (4,7)
A. Y-5. }(x-4)
O B. -2x+ 3y = 1
C. - 2x + 3y - 13
O D. 2x - 3y = 13

User Hslugs
by
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1 Answer

5 votes

Answer:


3y - 2x = 13

Explanation:

Given

Points (-14,-5) and (4,7)

Required

Find its linear equation in a standard form

To find the linear form, we start by calculating the slope of the line

This is calculated as thus:


m = (y_2 - y_1)/(x_2 - x_1)

Where
(x_1,y_1) = (-14,-5)\ and\ (x_2,y_2) = (4,7)

So,
m = (y_2 - y_1)/(x_2 - x_1) becomes


m = (7 - (-5))/(4 - (-14))


m = (7 + 5)/(4 + 14)


m = (12)/(18)

Simplify fraction to lowest term


m = (6*2)/(6*3)


m = (2)/(3)

The equation of the line can then be calculated using any of the given points;

Using


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


Where\ (x_1,y_1) = (-14,-5)\ and\ m = (2)/(3)

We have


(2)/(3) = (y-(-5))/(x-(-14))


(2)/(3) = (y+5)/(x+14)

Multiply both sides by 3


3 * (2)/(3) = (y+5)/(x+14) * 3


2 = (y+5)/(x+14) * 3


2 = (3(y+5))/(x+14)

Multiply both sides by x + 14


2 * (x + 14) = (3(y+5))/(x+14) * (x + 14)


2 * (x + 14) = 3(y+5)

Open brackets


2 * x + 2 * 14 = 3* y+ 3 * 5


2x + 28 = 3y+ 15

Subtract 2x from both sides


2x - 2x + 28 = 3y+ 15 - 2x


28 = 3y+ 15 - 2x

Subtract 15 from both sides


28 - 15 = 3y+ 15 - 2x - 15


28 - 15 = 3y - 2x + 15- 15


13 = 3y - 2x

Reorder


3y - 2x = 13

Hence, the equation of the line in standard form is
3y - 2x = 13

User Aknay
by
8.1k points

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