Question

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

E(-2, 2), F(5, 1)

Answer 1

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

now we sub
slope(m) = (1 -2) / (5 - (-2)
slope(m) = (-1) / (5 + 2)
slope(m) = -1/7

now we use y = mx + b
slope(m) = -1/7
use either of your points....(-2,2)....x = -2 and y = 2
now we sub
2 = -1/7(-2) + b
2 = 2/7 + b
2 - 2/7 = b
14/7 - 2/7 = b
12/7 = b

so your equation is : y = -1/7x + 12/7.....but we need it in standard form
Ax + By = C

y = -1/7x + 12/7 --- add 1/7 to both sides
1/7x + y = 12/7 -- cannot have fractions, so we will multiply everything by 7
x + 7y = 12