Question

Given the points A(1,4), B(3,3) C(7,1), use slope to determine if they are collinear (on the same line).

Answer 1

First, we need to calculate the slope

Firstly with the points A and B

(1,4)=(x1,y1)

(3,3)=(x2,y2)

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-4}{3-1}=\frac{-1}{2}=-\frac{1}{2}$

then with A and C

(1,4)=(x1,y1)

(7,1)=(x2,y2)

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-4}{7-1}=\frac{-3}{6}=-\frac{1}{2}$

then with C and B

(3,3)=(x1,y1)

(7,1)=(x2,y2)

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{7-3}=\frac{-2}{4}=-\frac{1}{2}$

because we obtain the same value of the slope we can say the points are collinear in other words the points are in the same line

the equation of the line is

$y=-\frac{1}{2}x+\frac{9}{2}$$y=-0.5x+4.5$

the expression above is the equation using