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2 years ago

Which is an equation of the line that passes through the points (–6, 3) and (2, 7)?

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

8 0

Step-by-step explanation:

the typical line equation is

y = ax + b

a is the slope. it is the ratio of "y coordinate change / x coordinate change".

b is the y-intercept (the y value when x = 0) indicating the point, where the line crosses the y-axis.

going from one to the other point

x changes by +8 (from -6 to 2).

y changes by +4 (from 3 to 7).

so, the slope a is +4/+8 = 1/2.

the semi-finished equation is

y = 1/2 x + b

for b we use one of the points in the equation and since for b. let's go for (2, 7) :

7 = 1/2 × 2 + b = 1 + b

6 = b

so, the full equation is

y = 1/2 x + 6

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Step-by-step explanation:

Step(I):-

1) a)

Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }

A - B = {1,3,5,7} - { 7,14,21}

A - B = { 1 , 3, 5}

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Given function y = 3 + x²+x³y³ ...(I)

By using derivative formulas

y = xⁿ

$\frac{dy}{dx} = n x^{n-1}$

Apply d/dx ( UV) = U V¹ + V U¹

Differentiating equation (I) with respective to 'x' , we get

$\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))$

$\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))$

$\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}$

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