Question

The line that passes through (1, 5) and (-2, 3) in standard form

Answer 1

Lets find the slope first by using the slope formula..
slope(m) = (y2 - y1) / (x2 - x1)
(1,5)...x1 = 1 and y1 = 5
(-2,3)...x2 = -2 and y2 = 3
now we sub
slope(m) = (3 - 5) / (-2 - 1)
slope(m) = -2/-3
slope(m) = 2/3

now that we have the slope(m), we need to find the y intercept(b)
y = mx + b
slope(m) = 2/3
you can use either of your points..
(1,5)...x = 1 and y = 5
now we sub
5 = 2/3(1) + b
5 = 2/3 + b
5 - 2/3 = b
15/3 - 2/3 = b
13/3 = b

so now we have : y = 2/3x + 13/3...however, we need it in standard form.
Ax + By = C

y = 2/3x + 13/3 -- multiply entire equation by 3
3y = 2x + 13 -- subtract 2x from both sides
-2x + 3y = 13 -- multiply by -1 to make x positive
2x - 3y = -13 <== standard form

Answer 2

any questions ?