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3 years ago

Give the following equation in point slopr form, what is the slope of the line?

Mathematics

1 answer:

AVprozaik [17]3 years ago

5 0

Answer:

Slope= 3

Step-by-step explanation:

y - 4= 3(x+6)

y - 4= 3x + 18 distributive property

y - 4(+4) = 3x + 18(+4)

cancel out the 4 with its oposite and apply to both sides.

y = 3x + 22 final answer

Remember the slope intersept equation... y=mx+b

m is slope

b means the y-intersept.

So the final slope of the line is 3. (demostrated by graph below)

<em>Program for graph: Desmos</em>

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Alan and his classmates performed a linear regression analysis on the data set shown below and found that the line of best fit t

stealth61 [152]

Answer:

C. $y=\frac{4}{5}x+7$

Step-by-step explanation:

Alan and his classmates found that the line of best fit through the data had the equation $y=-\frac{5}{4}x+18$

The slope of this line is $m=-\frac{5}{4}$

If a line would intersect this line of best fit at right angles, then the two lines are perpendicular to each other.

The slopes of perpendicular lines are negative reciprocals of each other,

Hence that line must have slope $\frac{-1}{-\frac{5}{4}} =\frac{4}{5}$

Therefore we look for a line whose slope is $\frac{4}{5}$ from the given options.

That line is the third option $y=\frac{4}{5}x+7$

5 0

3 years ago

A graph titled Swimmers at City Pool has Temperature (degrees Fahrenheit) on the x-axis, and swimmers on the y-axis. A trend lin

aniked [119]

Answer:

25 is the answer

7 0

3 years ago

Read 2 more answers

PLS ANSWER URGENT

san4es73 [151]

A) The given equation has no solution. The absolute value cannot be negative, but must be -9 in order for the equation to be satisfied.

b) |x -7| = 2 . . . . . . . the equation
Solution 1:
-2 = x -7
5 = x . . . . . . add 7
Solution 2
x -7 = 2
x = 9 . . . . . . add 7

The two numbers are {5, 9}

8 0

3 years ago

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

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3 years ago

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nekit [7.7K]

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3 years ago