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3 years ago

What is the slope between the points (4,-1) and (-4,3)?

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

The formula for slope is $\frac{rise}{run} = \frac{y2-y1}{x2-x1}$ .

Subtract y1 from y2. (y1= -1, y2 = 3)

3 - -1 = 4

Now subtract x1 from x2. (x1 = 4, x2 = -4)

-4 -4 = -8

Divide the difference between the y coordinates by the difference between the x coordinates.

$\frac{4}{-8}$ or 4 ÷ -8 = -0.5

<h2>Answer:</h2>

The slope between the two points is -0.5.

Hope this helps love :)

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lawyer [7]

Answer:

The difference quotient for $f(x)=3x^2$ is $3 h + 6 x$ .

Step-by-step explanation:

The difference quotient is a formula that computes the slope of the secant line through two points on the graph of f. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative and it is given by

$\frac{f(x+h)-f(x)}{h}$

So, for the function $f(x)=3x^2$ the difference quotient is:

To find $f(x+h)$ , plug $x+h$ instead of $x$

$f\left(x+h\right)=3 \left(h + x\right)^{2}$

Finally,

$\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{\left(3 \left(h + x\right)^{2}\right)-\left(3 x^{2}\right)}{h}$

$\frac{3\left(\left(h+x\right)^2-x^2\right)}{h} \\\\\frac{3(h^2+2hx+x^2-x^2)}{h} \\\\\frac{3h\left(h+2x\right)}{h}\\\\3h+6x$

The difference quotient for $f(x)=3x^2$ is $3 h + 6 x$ .

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Step-by-step explanation:

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I hope this helped!

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