Question

need help...

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(7, -3), (4, -8)

Answer 1

can you find the slope between the two points ?

Answer 2

yes....-8+3/4-7=-5/-3

Answer 3

and -5/-3 is 5/3 (the two minus signs make a plus)

now use the point slope formula

y - y0 = m ( x - x0)
where (x0,y0) is a point you know that is on the line, and m is the slope = 5/3 for this problem

can you replace x0, y0 and m with the correct numbers? what do you get ?

Answer 4

y+3=5/3(x-7)

Answer 5

yes... of course you could have used the other point ... in case you were wondering.

now we need to make it into standard form. there are no fractions in standard form.
to get rid of the 5/3, multiply both sides by 3, like this:

\[ 3(y+3) = 3 \cdot \frac{5}{3} \cdot (x-7)\]

can you distribute the 3 on the left side and the 5 on the right side ?

Answer 6

in case you did not know... 3/3 "cancels" (becomes 1, and multiply by 1 can be ignored)

Answer 7

distribute means multiply each term inside the parens. for example
3(y+3) means 3*y + 3*3
or 3y + 9

Answer 8

ok....3y+9=5x-35

Answer 9

any ideas what do to next ?

Answer 10

+ 5x on both sides??????????

Answer 11

almost. you want the 5x on the right side to "go away" you do that by adding -5x
because 5x take away 5x leaves nothing...
of course if you add -5x to the right side, you have to add -5x to the left side also.

what do you get?

Answer 12

will it be -5x+3y+9=-35

Answer 13

yes

Answer 14

3y+9=5x-35
-5x+3y +9 = 5x - 5x -35

or
-5x + 3y + 9 = -35

standard form is
Ax + By = C

(and A is positive)

you are almost done. you need to "move" the 9 to the other side. To do that add -9 to both sides, and simplify

Answer 15

so it will be 5x+3y=-26

Answer 16

one step at a time
-5x + 3y + 9 = -35

add -9 to both sides

Answer 17

-5x+3y+-9=-35+-9

-5x+3y=-44?????????

Answer 18

yes, but I would write it like this

first, the original equation: -5x + 3y + 9 = -35
then write in -9 on both sides: -5x + 3y + 9 + -9 = -35+-9
then simplify: 9-9 is 0 on the left side: -5x + 3y = -35 + -9
and -35 - 9 is -44 on the right side: -5x+3y=-44

Answer 19

now the last step.
we have
-5x+3y=-44
which matches
Ax + By = C
but the A is supposed to be positive. We have -5 which is negative

multiply both sides by -1:

-1(-5x+3y) = -1* -44
distribute the -1 on the left

what do you get ?

Answer 20

5x+3y=44

Answer 21

almost. distribute the -1 means multiply each term inside the parens by -1

try again
-1(-5x+3y) = 44

Answer 22

-1*-5=5 -1*3=-3 than-44*-1=44

which is 5x+-3y=44????

Answer 23

yes, exactly. but generally people write 5x + -3y as 5x - 3y (it means the same thing, but it looks nicer)

5x - 3y = 44

Answer 24

ok thank you for all the help.......:)

Answer 25

just to make sure we didn't make a mistake, we can test the other point (4, -8) in this equation:

5x - 3y = 44
5*4 + -3*-8 =? 44
20 +24 =? 44
44 = ? 44 yes, it worked.

Answer 26

ok....