Mathematics, 08.07.2019 05:50 pinkycupcakes3oxbqhx

Write an equation of the line passing through each of the following pairs of points. a) (−10, 4), (2, −5) b) (5, 7), (−6, −3)

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A) First find the slope of the two coordinates given.

Slope = y2 - y1 / x2 - x1

Substitute the values of the coordinates. It doesn't matter which coordinate is x1 or x2 as long as thereby value corresponds.

Slope = -5 - 4 / 2 - (-10)

Slope = -9 / 12

Slope = -3/4

Then, plug in either of the coordinates into the equation of a line.

y - y1 = m(x - x1)

y - 4 = -3/4(x - (-10)

y - 4 = -3/4(x + 10)

y - 4 = -3/4x - 7.5

y = -3/4x - 3.5

Check if using the other coordinate makes a difference.

y - (-5) = -3/4(x - 2)

y + 5 = -3/4x + 1.5

y = -3/4x - 3.5

The equation of a line for these coordinates is:

y = -3/4x - 3.5

2) Just apply the same concept for the second one :)

Answer from: 5nathanomadrid5

The required equation of the line passing through the coordinates (−10, 4), (2, −5) is 4y+3x = -14

The required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27

The formula for finding the equation of a line is expressed as:

$y-y_0=m(x-x_0)\\$

Given the coordinates (−10, 4), (2, −5)

Get the slope:

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

$m=\frac{-5-4}{2-(-10)} \\m=\frac{-9}{12}\\m=\frac{-3}{4}$

Get the required equation

$y-4=-3/4(x+10)\\4(y-4)=3(x+10)\\4y-16=-3x-30\\4y + 3x = -30+16\\4y+3x = -14\\$

b) For the equation of the line with the coordinates (5,7) and (-6, -3)

Get the slope

m = -3-7/-6-5

m = -10/-11

m = 10/11

The required equation will be:

y - 7 = 10/11(x-5)

11(y-7) = 10(x-5)\

11y - 77 = 10x - 50

11y - 10x = -50 + 77

11y - 10x = -27

Hence the required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27

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Answer from: Quest

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

Answer from: Quest

$a^b=\underbrace{a\cdot a\cdot \ldots \cdot a}_{b}$

a - base

b - exponent

$8^3=\underbrace{8\cdot 8 \cdot 8}_{3}$

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8

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