Question

Write this equation in standard form of each line passing through the two given points (2,3);(1,-2)

Answer 1

The given points
(x₁,y₁) = (2,3)
(x₂,y₂) = (1,-2)

There are 2 formulas we will use.
The first is formula to find the slope, and the second is formula to find the line equation.
To find the slope
m = (y₂ - y₁)/(x₂ - x₁)
To find the line equation
y - y₁ = m(x - x₁)

Find the slope, input the numbers to the formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (-2-3) / (1-2)
m = -5/-1
m = 5

Find the line equation, input the numbers to the formula
y - y₁ = m(x - x₁)
y - 3 = 5(x - 2)
5(x - 2) = y - 3
5x + 10 = y - 3
5x - y = -3 - 10
5x - y = -13

The equation of the line is
5x - y = -13