Question

Can someone please help me quickly?

Write the equation of the line that passes through (2, 2) and (6, 3) in standard form.

I know you have to get the slope, and the slope is 1/4. But then you have to do something else and that's where I'm stuck.. I have no idea what I'm supposed to do now...

Answer 1

y—y1=m(x—x1) (2,2) plug them in

y-2=1/4(x-2) or
you can plug in the other ordered pair (6,3)

y-3=1/4(x-6)

if you like --you can solve y
and put in this form y=mx+b

Answer 2

How do I solve y then, because I can't have it in that format.. I need it in y=mx+b ;-;

Answer 3

y-2=1/4(x-2) first mult each term inside pareetheses by 1/4 on RHS

y-2 = 1/4x-1/2 add 2 to both sides

y= 1/4x-1/2+4/2

y= 1/4x+3/2

Answer 4

(3 - 2) / (6 - 2) = 1/4 -- your correct with the slope

now we can either solve it by using y = mx + b and solve for b or we can use y - y1 = m(x - x1)

lets do y = mx + b
slope(m) = 1/4
(2,2) x = 2 and y = 2
now we sub
2 = 1/4(2) + b
2 = 1/2 + b
2 - 1/2 = b
4/2 - 1/2 = b
3/2 = b
therefore your line is : y = 1/4x + 3/2
Now we need standard form...
y = 1/4x + 3/2 (multiply the equation by 4)
4y = x + 6 (now subtract x)
-x + 4y = 6 (now multiply by -1 to make x positive)
x - 4y = - 6

or

y - y1 = m(x - x1)
slope(m) = 1/4
(2,2) x1 = 2 and y1 = 2
now we sub
y - 2 = 1/4(x - 2)
y - 2 = 1/4x - 1/2
y = 1/4x - 1/2 + 2
y = 1/4x - 1/2 + 4/2
y = 1/4x + 3/2 (subtract 1/4x from both sides)
-1/4x + y = 3/2 (multiply by 4)
-x + 4y = 6 (multiply by -1)
x - 4y = -6

you will arrive at the same answer either way you do it

Answer 5

Thank you so much Texas! :DD I can base myself off of that and finish my other questions now. c: Thank you again!

Answer 6

anytime :) glad to help