Question

A line passes through (-7, -5) and (-5, 4). a. Write an equation gor the line in point-slope form. b. Rewrite the equation in standard form using integers.
A. Y-5=9/2(x+7);-9x+2u=-53
B. Y+5=9/2(x-7);-9x+2y=53
C. Y+5=9/2(x+7);-9x+2y=53
D. Y+7=9/2(x+5);-9x+2y=31

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -7 &,& -5~) % (c,d) &&(~ -5 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{-5-(-7)}\implies \cfrac{4+5}{-5+7}\implies \cfrac{9}{2}$

$\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{9}{2}[x-(-7)] \\\\\\ \boxed{y+5=\cfrac{9}{2}(x+7)}\implies y+5=\cfrac{9}{2}x+\cfrac{63}{2}\impliedby \begin{array}{llll} \textit{and now we multiply}\\ \textit{both sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2y+10=9x+63\implies \boxed{\stackrel{\textit{standard form}}{-9x+2y=53}}$

just a quick note, multiplying both sides by the LCD, whatever it may be, simply gets rid of the denominators.