Question 1142403
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<pre>
First, calculate the slope.


    The formula for the slope of a straight line passing through two given points  ({{{x[1]}}},{{{y[1]}}})  and  ({{{x[2]}}},{{{y[2]}}})  is
        m = {{{(y[2]-y[1])/(x[2]-x[1])}}}.

    Substitute the given data  {{{x[1]}}} = 4,  {{{y[1]}}} = -2,  {{{x[2]}}} = 1, {{{y[2]}}} = 3  into the basic formula

        m = {{{(3-(-2))/(1-4)}}} = {{{5/(-3)}}} = {{{-5/3}}}.


Next, write an equation of the line having the slope  {{{-5/3}}}  and passing through the given point (4,-2).


    An equation of a straight line in a coordinate plane which has the slope m and passes through the given point  P = (a,b)  is 

        y - b = m*(x-a).     

    Substitute here  m = {{{-5/3}}},  a = 4,  b = -2,  and you will get

        y - (-2) = {{{(-5/3)*(x-4)}}},   or, equivalently,


        y + 4    = {{{(-5/3)*(x-4)}}}.


        Having the equation in this form, you can convert it to any other equivalent form you want.
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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Equation-for--a-straight-line-passing-through-two-given-points.lesson>Equation for a straight line in a coordinate plane passing through two given points</A>

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