Your answer would be A. positive linear association.

If we break this phrase down, we first get "positive", which we can see is true here as the graph is ascending towards the top right, that is, going upwards and 'forwards'. This is how we recognise lines with positive slopes, such as 3x or (1/2)x.

The word "linear" means a straight line, you can sort of see the word "line" in it, and so this is also true as the trend line is straight.

I hope this helps!

8 0

3 years ago

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the give

neonofarm [45]

Answer:

Equation of tangent:

$y = xe^{x}$

At point (1,0):

y = 2.713

Step-by-step explanation:

The equation of tangent line to the function can be calculated by taking the first derivative.

We have,

$y = xe^{x}-e^{x}\\\frac{dy}{dx}=\frac{d}{dx}[ xe^{x} ]-\frac{d}{dx} [e^{x}]\\$

Applying Product Rule:

d/dx [u.v] = (d/dx u) . (v) + (u) . (d/dx v)

Therefore,

$\frac{dy}{dx}=\frac{d}{dx}(x) . e^{x}+x .\frac{d}{dx}(e^{x})- \frac{d}{dx}(e^{x})\\\\\frac{dy}{dx}=(1)(e^{x})+(x)(e^{x})-e^{x}\\ \frac{dy}{dx}=xe^{x}\\\\$

The above equation is the equation of tangent line.

The point given is (1,0):

So,

$\frac{dy}{dx} = (1)e^{1}\\ \frac{dy}{dx} = e\\\frac{dy}{dx} = 2.713$

3 0

3 years ago