Question 146603


First let's find the slope through the points *[Tex \LARGE \left(\frac{1}{4},-\frac{1}{2}\right)] and *[Tex \LARGE \left(\frac{3}{4},6\right)]



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



{{{m=(6--1/2)/(3/4-1/4)}}} Plug in {{{y[2]=6}}}, {{{y[1]=-1/2}}}, {{{x[2]=3/4}}}, {{{x[1]=1/4}}}, , 



{{{m=(13/2)/(3/4-1/4)}}} Subtract {{{-1/2}}} from {{{6}}} to get {{{13/2}}}



{{{m=(13/2)/(1/2)}}} Subtract {{{1/4}}} from {{{3/4}}} to get {{{1/2}}}



{{{m=(13/2)*(2/1)}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{m=13}}} Multiply and reduce.



So the slope of the line that goes through the points *[Tex \LARGE \left(\frac{1}{4},-\frac{1}{2}\right)] and *[Tex \LARGE \left(\frac{3}{4},6\right)] is {{{m=13}}}



Now let's use the point slope formula:



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



{{{y--1/2=13(x-1/4)}}} Plug in {{{m=13}}}, {{{x[1]=1/4}}}, and {{{y[1]=-1/2}}}



{{{y+1/2=13(x-1/4)}}} Rewrite {{{y--1/2}}} as {{{y+1/2}}}



{{{y+1/2=13x+13(-1/4)}}} Distribute



{{{y+1/2=13x-13/4}}} Multiply



{{{y=13x-13/4-1/2}}} Subtract {{{1/2}}} from both sides. 



{{{y=13x-15/4}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



{{{y=13x-15/4}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(\frac{1}{4},-\frac{1}{2}\right)] and *[Tex \LARGE \left(\frac{3}{4},6\right)] is {{{y=13x-15/4}}}



 Notice how the graph of {{{y=13x-15/4}}} goes through the points *[Tex \LARGE \left(\frac{1}{4},-\frac{1}{2}\right)] and *[Tex \LARGE \left(\frac{3}{4},6\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,13x-15/4),
 circle(1/4,-1/2,0.08),
 circle(1/4,-1/2,0.10),
 circle(1/4,-1/2,0.12),
 circle(3/4,6,0.08),
 circle(3/4,6,0.10),
 circle(3/4,6,0.12)
 )}}} Graph of {{{y=13x-15/4}}} through the points *[Tex \LARGE \left(\frac{1}{4},-\frac{1}{2}\right)] and *[Tex \LARGE \left(\frac{3}{4},6\right)]