Prior Point Slope Form Next
This is the most useful line equation form as it only requires one point and a slope (of course the slope acquisition might require a second point) to write the line equation. $$y-y_{1}=m\left(x-x_{1}\right)$$ The point is $(x_1,y_1)$ and the slope is $m$.
Example: Given the parabola equation, $f(x)=x^2$, a point on the curve, $P=(1,1)$, and a slope, $m=2$, what is the line equation that goes through the point?
Example: Find the line with an angle of $30^{\circ}$ up from the $x$-axis that goes through the point $(1,2)$.