Write an equation in slope-intercept form for the line that passes through (6,- 3) and is parallel to y = -2x + 4.
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Parallel lines are lines with the same slope but different y-intercept.
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept.
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The given line is y=-2x+4. A line parallel to this would have the same slope, which is -2. To find the y-intercept, plug the point into an equation in point-slope form.
[tex]\displaystyle \text{Point-Slope Form} \rightarrow y-y_{1}=m(x-x_{1})[/tex]
m is the slope, and since the slope is the same as the given line, m will be equal to 2.
The line is supposed to pass through a point, which is written as (x, y). In this line, it is supposed to pass (6, -3). x₁ will be the x value of the point, and y₁ will be the y value of the point. That means x₁ is 6 and y₁ is -3.
Substitute the values into the formula:
[tex]y-y_{1}=m(x-x_{1}) \rightarrow y-(-3)=2(x-6)[/tex]
When subtracting a negative number from a number or variable, the sign will change, and the number will become positive.
[tex]y-(-3)=y+3[/tex]
Here is the new equation:
[tex]y-3=2(x-6)[/tex]
Distribute the 2 to everything in the parentheses. It will be 2 times x and 2 times -6. Remember that a positive number multiplied by a negative number is negative.
Positive(+) times(×) positive(+) = positive(+) Positive(-) times(×) negative(-) = negative(-) Positive(+) divided(÷) by positive(+) = positive(+) Positive(+) divided(÷) by negative(-) = negative(-)[tex]2 \times x=2x\\2 \times -6=-12\\\\2(x-6)=2x-12[/tex]
Rewrite the equation:
[tex]y-3=2x-12[/tex]
Lastly, you need to move -3 to the other side, as slope-intercept form is written as y=mx+b. You can move it by adding three(+3) to both sides, which is simply doing the opposite of it(-3+3=0).
[tex]\displaystyle y-3+3=2x-12+3[/tex]
[tex]y=2x-9[/tex]
The answer to your question is [tex]\bf \displaystyle y=2x-9[/tex].
On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(2, 3), and C(4, −1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.
The minimum total distance the employee may have driven before getting stuck in traffic is
miles.
Answer:
7.6 miles
Step-by-step explanation:
Given the coordinate points :
A(−3, 1), B(2, 3), and C(4, −1)
Distance (d) between A and B:
x1 = - 3 ; x2 = 2 ; y1 = 1 ; y2 = 3
d = √(x2 - x1)² + (y2 - y1)²
d = √(2 - (-3))² + (3 - 1)²
d = √25 + 4
d = 5.385 miles
BC :
d = √(x2 - x1)² + (y2 - y1)²
d = √(4 - 2)² + (-1 - 3)²
d = √2² + (-4²)
d = √4 + 16
d2 = 4.4721359 miles
(1/2) of d2 = 1/2 * 4.4721359 = 2.236 miles
Total distance = (5.385 + 2.236) miles
Total distance driven before getting stuck in traffic = 7.6 miles
At one gas station, gas costs $2.75 per gallon. Write an equation that relates the total cost, C , to the number of gallons of gas purchased, g
Answer:
C (g) = 2.75g
Eighteen 2.5 gallon buckets are needed to fill a cistern with water. Find the constant of variation. Please help! Thank you!
Given:
Eighteen 2.5 gallon buckets are needed to fill a cistern with water.
To find:
The constant of variation.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
Where, k is constant of variation.
In the given problem, water in cistern (w) is directly proportional to number of buckets (n).
[tex]w\propto n[/tex]
[tex]w=2.5n[/tex] (Capacity of each bucket is 2.5 gallons)
Therefore, the constant of variation is 2.5.
Answer:
45
Step-by-step
I just did 18 * 2.5!
It a simple answer!
The quantites are inversely so that means you multiply the numbers. Like 18 * 2.5. That's how I got 45
What are the variable term in this expression 6x² +3ry + 3z
Answer:
x y and z?
Step-by-step explanation:
HELP FIND THE SLOPE. pLEASEEEEEEEE
Answer:
the slope is undefined
PRE/POST ASSESSMENT
Hector was making a solution. He put the components of the solution into a
beaker. Hector wanted to increase the amount of his solution and at the same
time keep the composition of the solution the same. The new solution will have
84 kilograms of water.
What will be the mass of the sugar in the new solution, in kilograms?
Hector's Solution
Component
Mass
Sugar
9.6 kg
Salt
7.0 kg
A 24.6
Water
12.0 kg
B
39.6
с
49.0
D
67.2
E
98.0
Answer:
oh wow thats alot
Step-by-step explanation:
how do you do multiplication in 7th grade mathimatics
Answer:
Learn your timetables daily.
Step-by-step explanation:
You can find songs online to help you memorize and understand them in the simplest form.
Answer:
you should practice your timetables and do some math practice so you could understand other math like division.
Step-by-step explanation:
please help will mark brainliest if correct
Answer:
Step-by-step explanation:
∠A or ∠SAM
Complementary and supplementary angles (no visual)
Za and Zb are complementary angles. Za measures 55°.
What is the measure of Zb?
Stuck? Watch a video or use a hint.
Report a problem
Pi
Tea
7 of 7
Answer:
b=35°
Step-by-step explanation:
complementary angles add up to 90°
a+b=90°
55°+b=90°
-55 -55
b=35°
hopefully this helps :)
Express as a product: 1-2cos(2a)
I've been really struggling with this. Please help & explain it.
Answer:
(2sin a - 1)(2sin a + 1)
Step-by-step explanation:
Here, we want to express what is given as a product
Mathematically;
cos2a = 1-2sin^2A
So we have;
1-2(1-2sin^a)
= 1 - 2 + 4sin^2a
= 4sin^2a - 1
Using the difference of two squares, this is;
(2sin(a) - 1)(2sin a + 1)
Given B(17,5), C(11,-3), D(-1,2), and E(x,-6), find the value of x so that BC || DE
Answer: x = 7
Step-by-step explanation:
What’s the absolute value equation for |x+4|=12
Answer:
8 and -16...............
| x + 4 | = 12 <=> x + 4 = 12 hoặc -x - 4 = 12 <=> x = 8 hoặc x = -16
Most units in the metric system are based
of the power of
1
5
0.1
10
Answer:
10
Step-by-step explanation:
A small order of fries at Wendy’s has 90 more calories than the small order of fries at McDonald’s. If together they have 550 calories, how many calories are in the Wendy’s small order of fries?
Answer:
370
Step-by-step explanation:
can i get brainliest
meg has $20 in a savings account that earns 10% annually. the interest is not compounded. how much will she have in 1 year
Step-by-step explanation: 10% of 20 is 2 so 20 + 2 = 22.
Hope this helps! ;)
HELP!! Combining like terms with rational coefficients
− 2/1 (−3y+10)
Answer:
6y−20
Step-by-step explanation:
I need help answering this question!
Answer:
2x+7=-3+2x multiply what’s in the bracket by the negative sign
Collect like terms
2x-2x=-3-7, so
0=-10
Step-by-step explanation:
I hope this is the answer, if it helped please give me brainliest
write the linear equation from the given information in slope intercept form (-1,3); slope=-3
Answer:
y = -3xStep-by-step explanation:
The standard expression of equation of a line in slope-intercept form is expressed as;
y = mx+c
m is the slope
c is the intercept
Given
slope m = -3
Point (x, y) = (-1, 3)
x = -1 and y = 3
Get the intercept
To get the intercept c, we will substitute the given values into the equation above to have;
y = mx+c
3 = -3(-1)+c
3 = 3 + c
c = 3-3
c = 0
Substitute m = -3 and c = 0 into the equation above;
y = mx+c
y = -3x+0
y = -3x
Hence the required linear equation is y = -3x
If 1 1/2 cups of water fills 2/3 of a water bottle. How many cups of water are needed to fill 1 water bottle?
Answer:
I think its 2 1/4, sorry if i'm wrong
Step-by-step explanation:
Pls I need help with this geometry problem. It's due today.
Step-by-step explanation:
Yz / RT = SZ / ST
2X +2 / 3X -7 = 35 / 40= 7 / 8
8( 2x+2) = 7( 3x-7 )
16 x +16 = 21x 49
5x = 65
x =13
YZ = 2×13 +2 = 28
what is the slope of any line that is perpendicular to the line y+3=2/5(x-1)
PLEASE YALL
Answer:
-5/2
Step-by-step explanation:
the slope of a perpendicular line is the opposite reciprocal
What is the value of |−44|?
Answer:
44
Step-by-step explanation:
Answer:
44
Step-by-step explanation:
absolute value just makes the number positive
what is an art and a science that deals with the collection,organization,creative presentation and analysis of data? A.physics B.statistics C. biology D.sampling
Answer:
The answer is B. Statistics
Evaluate this
(help)
Answer:
D. [tex]\frac{1}{27}[/tex]
Step-by-step explanation:
[tex]3^{-3}[/tex] = [tex]\frac{1}{27}[/tex]. First you need to remove the negative exponent, to do this move the term into the denominator. [tex]\frac{3^{-3} }{1}[/tex] becomes [tex]\frac{1}{3^{3} }[/tex], then solve for [tex]3^{3}[/tex], which equals 27. So your answer is [tex]\frac{1}{27}[/tex].
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. a) Simplify the expression and explain each step. (2 points) 4 ( 3 x + 2 ) − 2 b) Factor the expression completely. (1 point) 20 b − 16
Answer:
Step-by-step explanation:
To simplify the expression:
4(3x+2) - 2
The first step is to open the brackets
= 4 * 3x + 4* 2 - 2
= 12x + 8 - 2
= 12x - 6
Factor out the above expression, we get;
= 6(2x - 1)
To factor out the expression:
20b - 16
the factor that can be divided by 20 and 16 without remainder is 4;
So, we have:
= 4(5b - 4)
-3 (x + 10)
HELP
PLEASE
Answer:
−3X−30
Step-by-step explanation:
Can a number be both rational and irrational? Why or why not?
Answer:
Step-by-step explanation:
If it is irrational, it can never be rational unless it is acted upon by something else like a power.
Pi, no matter what is done to it, can never be rational. Once a number is declared as irrational, that is what it remains.
The exterior angle of a regular polygon is 60°.
What is the name of the regular polygon?
Step-by-step explanation:
exterior angle = 60°
exterior angle = 360/n
60° = 360°/n
60n = 360°
n = 6
A regular polygon with 6 sides is a HEXAGON.
please please help me!!
Answer:
5x+7
Step-by-step explanation:
every time it goes up by 5 so if that's the case if you 12 and subtract 5 then that's your constant cause that is where it started.
I hope this is good enough:
Which of the following sets of numbers could NOT represent three sides of a triangle
Answer:
4, 10, 15
Step-by-step explanation:
Because 4 plus 10 is less than 15