Question

Complete the equation of the line through (1,4)(1,4)left parenthesis, 1, comma, 4, right parenthesis and (2,2)(2,2)left parenthesis, 2, comma, 2, right parenthesis.
Use exact numbers.
y=y=y, equals

Answer 1

The equation of the line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}$

In your case, the points are (1,4) and (2,2). Plug these values in the equation to get

$\dfrac{x-1}{2-1}=\dfrac{y-4}{2-4} \iff x-1=\dfrac{4-y}{2}$

We can rewrite the equation as

$2(x-1)=4-y \iff 2x-2=4-y \iff y=-2x+6$