Question 171387


First let's find the slope of the line through the points *[Tex \LARGE \left(2,-3\right)] and *[Tex \LARGE \left(4,-4\right)]



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(-4--3)/(4-2)}}} Plug in {{{y[2]=-4}}}, {{{y[1]=-3}}}, {{{x[2]=4}}}, and {{{x[1]=2}}}



{{{m=(-1)/(4-2)}}} Subtract {{{-3}}} from {{{-4}}} to get {{{-1}}}



{{{m=(-1)/(2)}}} Subtract {{{2}}} from {{{4}}} to get {{{2}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(2,-3\right)] and *[Tex \LARGE \left(4,-4\right)] is {{{m=-1/2}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y--3=(-1/2)(x-2)}}} Plug in {{{m=-1/2}}}, {{{x[1]=2}}}, and {{{y[1]=-3}}}



{{{y+3=(-1/2)(x-2)}}} Rewrite {{{y--3}}} as {{{y+3}}}



{{{y+3=(-1/2)x+(-1/2)(-2)}}} Distribute



{{{y+3=(-1/2)x+1}}} Multiply



{{{2y+6=-x+2}}} Multiply EVERY term by the LCD 2 to clear the fraction.



{{{2y+6+x=2}}} Add "x" to both sides.



{{{2y+x=2-6}}} Subtract 6 from both sides.



{{{x+2y=-4}}} Combine and rearrange the terms.




So the line that passes through (2,-3) and (4,-4) is {{{x+2y=-4}}}