06.09.2021

Find an equation of the line that goes through the points (8,-45) and (2,-9). Write your answer in the form y = mx + b.

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09.07.2023, solved by verified expert
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Linear Equations

Linear equations are commonly organized in slope-intercept form:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

m = slopeb = the y-intercept (the value of y when x=0)

To find the equation of a line given two points:

Determine the slope of the line using the slope formulaPlug the slope into Find an equation of the line that goes through, №18011084, 06.09.2021 08:15Determine the y-intercept by solving for bPlug the y-intercept back into the equationSolving the Question

We're given:

The line passes through the points (8,-45) and (2,-9)

First, determine the slope using the following formula:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15 where the given points are Find an equation of the line that goes through, №18011084, 06.09.2021 08:15 and Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

⇒ Plug in the given points (8,-45) and (2,-9):

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

Therefore, the slope of the line is -6. Plug this into Find an equation of the line that goes through, №18011084, 06.09.2021 08:15 as m:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

Now, determine the y-intercept:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

⇒ Plug in one of the given points as (x,y) and solve for b:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

Therefore the y-intercept of the line is 3. Plug this back into Find an equation of the line that goes through, №18011084, 06.09.2021 08:15:

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

Answer

Find an equation of the line that goes through, №18011084, 06.09.2021 08:15

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Mathematics
Step-by-step answer
P Answered by Specialist
Linear Equations

Linear equations are commonly organized in slope-intercept form:

y=mx+b

m = slopeb = the y-intercept (the value of y when x=0)

To find the equation of a line given two points:

Determine the slope of the line using the slope formulaPlug the slope into y=mx+bDetermine the y-intercept by solving for bPlug the y-intercept back into the equationSolving the Question

We're given:

The line passes through the points (8,-45) and (2,-9)

First, determine the slope using the following formula:

m=\dfrac{y_2-y_1}{x_2-x_1} where the given points are (x_1,y_1) and (x_2,y_2)

⇒ Plug in the given points (8,-45) and (2,-9):

m=\dfrac{-45-(-9)}{8-2}\\\\m=\dfrac{-45+9}{8-2}\\\\m=\dfrac{-36}{6}\\\\m=-6

Therefore, the slope of the line is -6. Plug this into y=mx+b as m:

y=-6x+b

Now, determine the y-intercept:

y=-6x+b

⇒ Plug in one of the given points as (x,y) and solve for b:

-9=-6(2)+b\\-9=-12+b\\3=b

Therefore the y-intercept of the line is 3. Plug this back into y=-6x+b:

y=-6x+3

Answer

y=-6x+3

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
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P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
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P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
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P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

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