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3 years ago

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What is the equation of a line that has a slope of −12 and a y-intercept of 3? Express your answer in slope-intercept form.

1 answer:

Elena L [17]3 years ago

6 0

If given the slope and y-intercept, you can directly get the slope intercept form as

y = -12x + 3

You might be interested in

Solve the system of linear equations using multiplication.

Anna71 [15]

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$ .

We can now find $x$ given that $y=-1$ using the equation $x=7-y$ .

Let's do that.

$x=7-y$ with $y=-1$ :

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$ :

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$ :

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

5 0

3 years ago

Read 2 more answers

Victoria recently switched to a new electric company. If she uses between 0 and 400 kilowatt-hours (kWh) of electricity per mont

Gekata [30.6K]

Answer:

see the explanation

Step-by-step explanation:

<em><u>The question is </u></em>

Identify the domain and the range, using words and inequalities

Let

x -----> the number of kilowatt-hours (kWh) of electricity per month

y ----> the price per month

we know that

Part 1) For the value of x between 0 kWh and 400 kWh

$0\ kWh \leq x < 400\ kWh$

The price is equal to

$y=\$30$

therefore

The domain is the interval ------> [0,400)

The domain is all real numbers greater than or equal to 0 kWh and less than 400 kWh

The range is ($30)

The range is equal to $30

Part 2) For the value of x equal to 400 kWh or more per month

$x\geq 400\ kWh$

The domain is the interval -----> [400, infinite)

The domain is all real numbers greater than or equal to 400 kWh

The price is

$y=0.097x$

<em>Find the range</em>

For x=400 kWh

$y=0.097(400)=\$38.8$

so

$y\geq \$38.8$

The range is the interval -----> [38.8, infinite)

7 0

3 years ago

Use technology and the given confidence level and sample data to find the confidence interval for the population mean mu . assum

attashe74 [19]

To solve for the confidence interval for the population mean mu, we can use the formula:

Confidence interval = x ± z * s / sqrt (n)

where x is the sample mean, s is the standard deviation, and n is the sample size

At 95% confidence level, the value of z is equivalent to:

z = 1.96

Therefore substituting the given values into the equation:

Confidence interval = 3 ± 1.96 * 5.8 / sqrt (51)

Confidence interval = 3 ± 1.59

Confidence interval = 1.41, 4.59

Therefore the population mean mu has an approximate range or confidence interval from 1.41 kg to 4.59 kg.

6 0

3 years ago

A student needs to make a square cardboard piece. The cardboard should have a perimeter equal to at least 92 inches. The functio

Illusion [34]

Answer:

$s\geq 23$

Step-by-step explanation:

We are given that a student needs to make a square cardboard piece.

Perimeter of cardboard should be equal to atleast 92 inches

We have to find that which shows reasonable domain for f(s)

Let s be the side of square cardboard

We know that perimeter of square =f(s=) $4\times side$

Then, perimeter of cardboard= $4s$

$4s\geq 92$

Dividing by 4 on both sides

$s\geq 23$

Hence, the domain of function $[23,\infty)$

Therefore, option d is true.

Answer:d: $s\geq 23$

6 0

4 years ago

Find the midpoint of the segment with the given endpoints. (9,9) and (-1,- 3)

GenaCL600 [577]

Answer: (4, 3)

Step-by-step explanation:

The formula for coordinate of the mid point is given as :

Mid point = ( $\frac{x_{2}+x_{1}}{2}$ , $\frac{y_{2}+y_{1}}{2}$ )

$x_{1}$ = 9

$x_{2}$ = -1

$y_{1}$ = 9

$y_{2}$ = -3

Substituting the values into the formula , we have :

Mid-point = ( $\frac{-1+9}{2}$ , $\frac{-3+9}{2}$ )

Mid-point = ( $\frac{8}{2}$ , $\frac{6}{2}$ )

Mid - point = ( 4 , 3)

8 0

3 years ago