Question

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

Answer 1

slope:

m = (y2 - y1)/(x2 - x1)

m = (0 - 7)/(-6 - 2)

m = -7/(-8)

m = 7/8

Answer 2

Now use this slope, and the first point, to find the y-intercept to find the slope intercept form

y = mx + b

y = (7/8)x + b

7 = (7/8)(2) + b

7 = 14/8 + b

7 - 14/8 = b

7*(8/8) - 14/8 = b

56/8 - 14/8 = b

(56 - 14)/8 = b

42/8 = b

21/4 = b

b = 21/4

So the equation in slope intercept form is

y = 7/8x + 21/4

with me so far? let me know when you want me to continue (to convert to standard form)

Answer 3

okay yeah i think i follow

Answer 4

any parts you're stuck on?

Answer 5

no i understand slope intercept form well, just not standard form

Answer 6

alright, let's continue then

Answer 7

the LCD of 7/8 and 21/4 is 8

Answer 8

so multiply EVERY term by the LCD 8 to get

y = 7/8x + 21/4

8*y = 8*(7/8x) + 8*21/4

8y = 56/8x + 168/4

8y = 7x + 42


now move over the x term

8y = 7x + 42

8y - 7x = 42

-7x + 8y = 42

finally, make the x term positive and you do this by multiplying both sides by -1


-7x + 8y = 42

-1*(-7x + 8y) = -1*42

7x - 8y = -42

Answer 9

so the equation in standard form is 7x - 8y = -42

Answer 10

thats not an answer option

Answer 11

hmm what are your choices?

Answer 12

-7x + 8y = 42
-7x - 8y = 42
-7x + 8y = -42
8x + 7y = 42

Answer 13

I see

Answer 14

so they left x alone

Answer 15

so ignore the last 3 steps

Answer 16

so what is the final answer

Answer 17

-7x + 8y = 42?

Answer 18

good

Answer 19

thank you so much for your help

Answer 20

you're welcome