Question 615924
First let's find the slope of the line through the points *[Tex \LARGE \left(3,4\right)] and *[Tex \LARGE \left(5,7\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,4\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,7\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=7}}}.



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



{{{m=(7-4)/(5-3)}}} Plug in {{{y[2]=7}}}, {{{y[1]=4}}}, {{{x[2]=5}}}, and {{{x[1]=3}}}



{{{m=(3)/(5-3)}}} Subtract {{{4}}} from {{{7}}} to get {{{3}}}



{{{m=(3)/(2)}}} Subtract {{{3}}} from {{{5}}} to get {{{2}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(3,4\right)] and *[Tex \LARGE \left(5,7\right)] is {{{m=3/2}}}



Now let's use the point slope formula:



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



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



{{{y-4=(3/2)x+(3/2)(-3)}}} Distribute



{{{y-4=(3/2)x-9/2}}} Multiply



{{{y=(3/2)x-9/2+4}}} Add 4 to both sides. 



{{{y=(3/2)x-1/2}}} 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>.



So the equation that goes through the points *[Tex \LARGE \left(3,4\right)] and *[Tex \LARGE \left(5,7\right)] is {{{y=(3/2)x-1/2}}}



So the slope is {{{3/2}}} and the y-intercept is <img src="http://latex.codecogs.com/png.latex?\large \dpi{120} \left(0,- \frac{1}{2} \right )" title="\LARGE \dpi{120} \left(0,- \frac{1}{2} \right )" />