Question

Write the standard form of the line that passes through the given points (6,1) and (5,4)

Answer 1

The standard form:

$Ax+By=C$

The point-slope form:

$y-y_1=m(x-x_1)$

m - slope

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (6, 1) and (5, 4). Substitute:

$m=\dfrac{4-1}{5-6}=\dfrac{3}{-1}=-3$

$y-1=-3(x-1)$      use distributive property

$y-1=-3x+3$          add 1 to both sides

$y=-3x+4$         add 3x to both sides

$\boxed{3x+y=4}$