A line passes through both (\blue{X1}, \blue{Y1}) and
(\green{X2}, \green{Y2}).
Express the equation of the line in point slope form.
y - {}{} = {}(x - {})
The formula to find the slope is: m = \dfrac{(y_{1} - y_{2})}{(x_{1} - x_{2})}.
So, by plugging in the numbers, we get:
\dfrac{\blue{Y1} - negParens(Y2, "green")}
{\blue{X1} - negParens(X2, "green")} =
\pink{\dfrac{Y1 - Y2}{X1 - X2}} =
\pink{SLOPE_FRACTION}
Select one of the points to substitute for x_{1} and y_{1} in the point slope formula.
Either (y - \blue{Y1}) = \pink{SLOPE_FRACTION}(x - \blue{X1}),
or (y - \green{Y2}) = \pink{SLOPE_FRACTION}(x - \green{X2}).
Given the following values, find the equation of the line.
\begin{eqnarray}
x_{1} &=& \blue{X1},\quad &f(x_{1}) = \blue{Y1} \\
x_{2} &=& \green{X2},\quad &f(x_{2}) = \green{Y2}
\end{eqnarray}
f(x) is just a fancy term for y.
So one point on the line is (\blue{X1}, \blue{Y1}).
Another is (\green{X2}, \green{Y2}).
The slope of a line is \pink{SLOPE_FRACTION}
and its y-intercept is \blue{Y1}.
The y-intercept is the value of y when x = 0.
So the line goes through the point, (\blue{X1}, \blue{Y1}).
Thus, the solution in point slope form can be written as:
(y - \blue{Y1}) = \pink{SLOPE_FRACTION}(x - \blue{X1})