Question

will reward medal for help.

Indicate in standard form the equation of the line passing through the given points.

A(4, 1), B(5, 2)

I cant seem to nail this problem down.
is this the right formula to solve it? (its an example)
https://cornerstonetx.ignitiaschools.com/media/g_geo_2013/9/l9hg85.gif

Answer 1

first we find the slope using the slope formula
slope(m) = (y2 - y1) / (x2 - x1)
(4,1)....x1 = 4 and y1 = 1
(5,2)...x2 = 5 and y2 = 2
now we sub to find the slope
slope(m) = (2 - 1) / (5 - 4)

can you finish and find the slope....then we can continue

Answer 2

y-1= 1/1 (x-4)

am i on the right track. i have no idea

Answer 3

ok...your using point slope formula....thats fine, we can use that or we can just use slope intercept formula, which is y = mx + b....how do you wish to continue ?

Answer 4

the simple easy way.

Answer 5

y = mx + b ....I usually just use this formula unless specifically asked to use point slope formula.

y = mx + b
slope(m) = 1/1, or you can just put 1
you can use either of your points...(4,1)....x = 4 and y = 1
now we sub...we are looking for b, the y intercept, since we already know the slope

y = mx + b
1 = 1(4) + b
1 = 4 + b
1 - 4 = b
-3 = b

so our equation in slope intercept form is : y = 1x - 3, or you can just put y = x - 3

do you understand so far ? Any questions ? Let me know, if not, we can continue

Answer 6

i think i got it

Answer 7

that is slope intercept form, but we need it in standard form : Ax + By = C

we have : y = x - 3 ----subtract x from both sides
-x + y = -3 --- multiply everything by -1 to make x positive
x - y = 3 --- standard form

Answer 8

any questions ?

Answer 9

im still confused

Answer 10

with what part ?

Answer 11

talk to me and let me help you

Answer 12

do you understand how to find the slope ?

Answer 13

do you understand how to turn an equation from slope intercept to standard ?

Answer 14

so our equation in slope intercept form is : y = 1x - 3, or you can just put y = x - 3

how did you get that

Answer 15

we found that our slope(m) was 1.

slope intercept form is : y = mx + b
we already know that slope (m) = 1
now we use either of our points....(4,1)....x = 4 and y = 1
now we sub our info into y = mx + b to find b, the y intercept
y = mx + b
1 = 1(4) + b
1 = 4 + b
1 - 4 = b
-3 = b

now all you have to do is sub in your slope(m) and you y intercept(b)
y = 1x - 3...or you can just put y = x - 3

did that help any ??

Answer 16

oh, yes, now i see

Answer 17

even if you used point slope formula : y - y1 = m(x - x1)
slope(m) = 1
(4,1)...x1 = 4 and y1 = 1

y - 1 = 1(x - 4) --- distribute through the parenthesis
y - 1 = x - 4 --- add 1 to both sides
y = x - 4 + 1
y = x - 3....same thing

Answer 18

to turn it to standard form Ax + By = C

y = x - 3 --- subtract x from both sides
-x + y = -3 -- you cannot have a negative x, so multiply everything by -1
-x(-1) + y(-1) = -3(-1)
x - y = 3 --- standard form

Answer 19

remember, a neg times a neg is a positive, and a pos times a neg is a neg

Answer 20

so you cant use point formula to get the standard form?

Answer 21

and even thought the x and y do not have a number in front of them, it is understood to be 1.

yes...you can use point slope...because you will arrive at the same answer...because you are turning point slope to slope intercept and then to standard.

Answer 22

I just prefer to leave out the point slope and just do slope intercept....it just skips a step that is not necessarily needed

Answer 23

thanks!

Answer 24

sure thing :)