The equation of a line is based on two simple questions: "How much y changes when you add 1 to x?" and "How much is y when x=0?"
First, it's important to know that a linear equation has a general formula defined by y = m*x + n.
Having those questions in mind, we can find the slope (m) of the line, that is how much y changes when you add 1 to x:
m = (D_x)/(D_y), with D_x being the difference in x and D_y being the difference in y.
D_x = -3-(1/2) = -3-1/2 = -7/2
D_y = -1-(2) = -1-2 = -3
m = (-7/2)/-3 = -7/2 * -1/3 = (-7*-1)/(2*3) = 7/6
Now, we need to find y_0, that is the value of y when x=0:
Since when x=-3, y=-1, we can sum the slope 3 times (since -3 +3 = 0) in y:
y_0 = -1 + 3*(7/6) = -1+21/6 = - 6/6+21/6 = 15/6
We now have the slope and the y_0 (or n) value, we apply in the main formula of a linear equation:
y = m*x + n = 7/6 * x + 15/6 = (7x + 15)/6
