Question

Find the equation, in standard form, of the line passing through the points (3,-4) and (5,1).

5x-2y=23
y=5/2x-23/2
5x+2y=23
2x-3y=9

Answer 1

first we need to find the slope using the slope formula...
slope(m) = (y2 - y1) / (x2 - x1)
(3,-4) x1 = 3, y1 = -4
(5,1) x2 = 5 and y2 = 1
now lets sub
slope(m) = (1 - (-4) / (5 - 3)
m = (1 + 4)/2
m = 5/2
the slope is 5/2
you still with me ? Any questions so far ?

Answer 2

yes, i understand the slope. i am just having trouble taking y = 5/2x+23/2 and putting it in standard form

Answer 3

Now we will use y = mx + b formula
slope(m) = 5/2
(5,1) x = 5 and y = 1
now we sub
y = mx + b
1 = 5/2(5) + b
1 = 25/2 + b
1 - 25/2 = b
2/2 - 25/2 = b
-23/2 = b

making our equation : y = 5/2x - 23/2
now we will put it in standard form
y = 5/2x - 23/2 (multiply the entire equation by the LCD, which is 2)
2y = 5x - 23 (subtract 5x from both sides)
-5x + 2y = -23 (now multiply the equation by -1 to make x positive)
5x - 2y = 23 <-- standard form

Answer 4

any questions ?

Answer 5

no, thank you. I understand now. :)

Answer 6

glad I could help :)