Question

the point slope form of the equation of a line that passes through the point (-4,3) and (12,1) is y-1=1/4(x-12). what is the standard form of the equation for this line?

Answer 1

in short, the standard is just the same thing, expanded and with only the constant on the right-hand-side,


`\bf \stackrel{point-slope~form}{y-1=\cfrac{1}{4}(x-12)}\implies y-1=\cfrac{1}{4}x-3\implies \stackrel{slope-intercept~form}{y=\cfrac{1}{4}x-2} \\\\\\ \stackrel{standard~form}{-\cfrac{1}{4}x+y=-2}`