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3 years ago

Which of the following equations represents a linear function?

Mathematics

1 answer:

liubo4ka [24]3 years ago

4 0

A linear equation has maximum power of a variable(variables) 1.

In order to find the linear equations we need to check the equations with variable with power one.

Also the variable should be in numerator only.

Let us check option one by one:

a-y=√x + 1 we have a radical on x.

Therefore, it's not a linear equation.

b-y=1/x

We have x in the denominator of 1.

Therefore, it's not a linear equation.

c-y=x^2 +4

We have power 2 of x. Therefore, it's not a linear equation.

d-y = -2/3x + 4/3.

We have x and y powers only 1.

Therefore, it's the only linear equation.

<h3>Therefore, correct option is D option. d-y = -2/3x + 4/3</h3>

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 6xy + 12y2 = 28, (2,

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The equation of the tangent line is $y = -\frac{5}{18}\cdot x +\frac{14}{9}$ .

Step-by-step explanation:

Firstly, we obtain the equation for the slope of the tangent line by implicit differentiation:

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$2\cdot (x + 3\cdot y) + 6\cdot (x + 4\cdot y) \cdot y' = 0$

$6\cdot (x + 4\cdot y) \cdot y' = -2\cdot (x+3\cdot y)$

$y' = -\frac{1}{3}\cdot \left(\frac{x + 3\cdot y}{x + 4\cdot y} \right)$ (1)

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$y' =-\frac{5}{18}$

By definition of tangent line, we determine the intercept of the line ( $b$ ):

$y = m\cdot x + b$

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If we know that $(x,y) = (2,1)$ and $m = -\frac{5}{18}$ , then the intercept of the tangent line is:

$b = 1 - \left(-\frac{5}{18} \right)\cdot (2)$

$b = \frac{14}{9}$

The equation of the tangent line is $y = -\frac{5}{18}\cdot x +\frac{14}{9}$ .

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