Question

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

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

Answer 1

find the slope first by 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
slope(m) = (2 - 1) / (5 - 4)
slope(m) = 1

now we use y = mx + b form...we already found the slope(m), so now we will look for b, the y intercept.
slope(m) = 1
you can use either of your sets of points...(4,1)..x = 4 and y = 1
now we sub
y = mx + b
1 = 1(4) + b
1 = 4 + b
1 - 4 = b
-3 = b

our equation is : y = x - 3
but we need it in standard form : Ax + By = C
y = x - 3 -- subtract x from both sides
-x + y = -3 -- multiply by -1 to make x positive
x - y = 3 <== standard form