This is so confunsing, can someone please help?
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a,1) is on the line.
I thought it had something to do with finding the slope . . .
Hello,
if you have 2 separate points $\displaystyle P_1(x_1 , y_1)~\text{and}~P_2(x_2 , y_2)$ which lay on a line then the equation of the line is:
$\displaystyle \frac{y - y_1}{x - x_1} = \underbrace{\frac{y_2 - y_1}{x_2 -x_1}}_{\text{slope of the line}}$ . this formula is called two-points-formula of a straight line.
Plug in the coordinates of the points. Don't forget with your problem x = a and y = 1. You'll get:
$\displaystyle \frac{1 - 7}{a - 3} = \frac{9 - 7}{-4 - 3}$ . Solve for a:
$\displaystyle \frac{-6}{a-3} = \frac{2}{-7}~\Longrightarrow~42 = 2a - 6 ~\Longrightarrow~ 2a = 48 ~\Longrightarrow ~ \boxed{a = 24}$