Mathematics, 28.08.2019 12:30 jasmine12314

Determine the standard form of the equation of the line that passes through (6,0) and (2,- . determine the standard form of the equation of the line that passes through (-5,0) and (0,-9). determine the standard form of the equation of the line that passes through (-7,8) and (0,2). determine the standard form of the equation of the line that passes through (0,5) and (4,0)

Answers: 2

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Answer from: JEThompson6416

Part 1) 7x-4y=42

Part 2) 9x+5y=-45

Part 3) 6x+7y=14

part 4) 5x+4y=20

Step-by-step explanation:

we know that

The standard form of the equation of the line is equal to

Ax + By = C

where

A is a positive integer

B, and C are integers

Part 1) Determine the standard form of the equation of the line that passes through (6,0) and (2,-7)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Substitute the values

$m=\frac{-7-0}{2-6}$

$m=\frac{-7}{-4}$

$m=\frac{7}{4}$

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=\frac{7}{4}$

Point (6,0)

substitute

$y-0=\frac{7}{4}(x-6)$

$y=\frac{7}{4}x-\frac{42}{4}$

Multiply by both sides

4y=7x-42

convert in standard form

7x-4y=42

Part 2) Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Substitute the values

$m=\frac{-9-0}{0+5}$

$m=-\frac{9}{5}$

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{9}{5}$

Point (-5,0)

substitute

$y-0=-\frac{9}{5}(x+5)$

$y=-\frac{9}{5}x-9$

Multiply by both sides

5y=-9x-45

convert in standard form

9x+5y=-45

Part 3) Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Substitute the values

$m=\frac{2-8}{0+7}$

$m=-\frac{6}{7}$

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{6}{7}$

Point (0,2)

substitute

$y-2=-\frac{6}{7}(x-0)$

$y=-\frac{6}{7}x+2$

Multiply by both sides

7y=-6x+14

convert in standard form

6x+7y=14

Part 4) Determine the standard form of the equation of the line that passes through (0,5) and (4,0)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Substitute the values

$m=\frac{0-5}{4-0}$

$m=-\frac{5}{4}$

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

$m=-\frac{5}{4}$

Point (0,5)

substitute

$y-5=-\frac{5}{4}(x-0)$

$y=-\frac{5}{4}x+5$

Multiply by both sides

4y=-5x+20

convert in standard form

5x+4y=20

Answer from: Quest

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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