Question

Which is an equation of the given line in standard form?

A. -6x+5y=13
B. -6x+7y=-11
C. -6x+7y=11
D. -7x+6y=-11

Answer 1

The slope: $m=\dfrac{y_2-y_1}{x_2-x_1}$

The coordinates of the points:
$(-3;\ -1)\to x_1=-3;\ y_1=-1;\ \left(\dfrac{1}{2};\ 2\right)\to x_2=\dfrac{1}{2};\ y_2=2$

Substitute: $m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}$

We have: $y=\dfrac{6}{7}x+b$

Substitute the coordinates of the point (-3; -1) to the equation of the line:

$-1=\dfrac{6}{7}\cdot(-3)+b\\\\-1=-\dfrac{18}{7}+b\ \ \ |+\dfrac{18}{7}\\\\b=\dfrac{11}{7}$

Therefore we have:
$y=\dfrac{6}{7}x+\dfrac{11}{7}\ \ \ |\cdot7\\\\7y=6x+11\ \ \ |-6x\\\\\boxed{-6x+7y=11}$

Answer: C. -6x + 7y = 11