Question

Which equation represents a line that passes through (2,-1/2) and has a slope of 3?

Answer 1

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-(1)/(2)})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left( -(1)/(2) \right)}=\stackrel{m}{3}(x-\stackrel{x_1}{2})\implies y+\cfrac{1}{2}=3x-6 \\\\\\ y=3x-6-\cfrac{1}{2}\implies y=3x-\cfrac{13}{2}`

Answer 2

Using y = mx + c where m is the slope and c is the y-intercept
we can write y = 3x + c
Substitute for the coordinates of the given point gives
-1/2 = 3*2 + c
so c = -1/2 - 6 = -13/6

y = 3x - 13/2