Question

Which line has a slope of 5/8 and goes through the point (2,-3)?

Answer 1

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad \qquad \qquad slope = m\implies \cfrac{5}{8} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{5}{8}(x-2) \\\\\\ y+3=\cfrac{5}{8}x-\cfrac{5}{4}\implies y=\cfrac{5}{8}x-\cfrac{5}{4}-3\implies y=\cfrac{5}{8}x-\cfrac{17}{4}$

$\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8y=5x-34}\implies -5x+8y=-34 \\\\\\ \stackrel{\textit{multiplying both sides by -1}}{5x-8y=34}\impliedby standard~form$

bear in mind that in a standard form of a linear equation

the variables are both on the left side, "x" before the "y" usually.

"x" cannot have a negative coefficient.

all coefficients and constants must be integers.