Question

Write the equation of the line that passes through the points (3,4) and (1,5)

Answer 1

Hi,

$y= -\frac{1}{2} x+b$

Answer 2

Given points
(x₁,y₁) = (3,4)
(x₂,y₂) = (1,5)

FIRST
Find the slope of the line. This is general formula to determine the slope
m = (y₂ - y₁)/(x₂ - x₁)

Plug in the numbers to the formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (5 - 4)/(1 - 3)
m = 1/(-2)
m = -1/2

SECOND
Determine the line equation
This is general formula to determine the line equation
y - y₁ = m(x - x₁)

Plug in the numbers
y - 4 = -1/2 (x - 3)
y - 4 = (-1/2)x + 3/2
y = (-1/2)x + 3/2 + 4
y = (-1/2)x + 11/2
(this is the equation of the line)