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3 years ago

Write the equation of a line with a slope of 7 and a y-intercept of -3. Put the equation in slope-intercept form.

Mathematics

1 answer:

Rina8888 [55]3 years ago

7 0

Answer:

y=7x-3

Step-by-step explanation:

y=mx+b

m is the slope, so replace m with 7

b is the t-intercept so replace b with the -3.

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Your friend won't get many stars like this! What changes would you make to the equation to help your friend collect all the star

algol [13]

The required equation that represents the line of best fit is y = 2x + 4

<h3>Finding the equation of a line of best fit.</h3>

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.

Using the following points (4, 12) and (2, 8)

The equation of the line will be in the form y = mx + b

where

m is the slope

b is the y-intercept

Determine the slope

Slope = y2-y1/x2-x1

Slope = 8-12/2-4
Sope = -4/-2
Slope = 2

Determine the y-intercept

Using the coordinate point (2, 8) and m = 2

8 = 2(2) + b

b = 8 - 4

b = 4

Hence the required equation that represents the line of best fit is y = 2x + 4

Learn more on line of best fit here: brainly.com/question/17013321

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6 0

2 years ago

Help me 5 and 6 plzzzzzz

Veronika [31]

5. It is 110 degrees
6. It is 137 degrees

5 0

4 years ago

Lianne is saving to buy a DVD player that costs 2 1\2 times her weekly allowance. If she spends 3\4 of her allowance on other th

ahrayia [7]

Answer:

She will take 10 weeks to save the money for the DVD player

Step-by-step explanation:

Let w = Lianne's weekly allowance.

The DVD player costs 2 1/2 times her weekly allowance, thus

DVD cost = 5/2w

She gets w every week but spends 3/4w on other things, thus the remaining money is

Weekly savings =w - 3/4w = 1/4w

To know the number of weeks needed, we divide the DVD cost by the weekly savings:

$\displaystyle N = \frac{\frac{5}{2}}{\frac{1}{4}}$

Operating:

$\displaystyle N = \frac{5}{2}*\frac{4}{1}$

N = 10

She will take 10 weeks to save the money for the DVD player

3 0

3 years ago

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

the shorter leg of a right triangle is 8 inches shorter ybsn the longer leg. the hypotenuse is 8 inches longer thsn the longer l

Artyom0805 [142]

Answer:

Short leg = 24inches

Long leg = 32inches

Hypotenuse = 40inches

Step-by-step explanation:

Given:

shorter leg is 8inches shorter than the longer leg
hypotenuse is 8inches longer than the longer leg
longer leg = x inches

Pythagorean Theorem:

a²+b²=c² → (x-8)²+ x² = (x+8)²

Solving for both sides:

x² - 16x+ 64 + x² = x²+ 16x + 64

More Painful Solving:

x² - 32x = 0

x(x-32) = 0

x=0 or 32

Can't use the 0 so we trash it!

x=32

add 8 to get the hypotenuse and subtract 8 to get the short leg

8 0

3 years ago