Question 1102491
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Find the equation of the line joining the points (2,11) and (4,17) 
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<pre>
First, calculate the slope.


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

    Substitute the given data  {{{x[1]}}} = 2,  {{{y[1]}}} = 11,  {{{x[2]}}} = 4, {{{y[2]}}} = 17  into the basic formula
        m = {{{(17-11)/(4-2)}}} = {{{6/2}}} = 3.


Next, find an equation of the line having the slope 3 and passing through the given point (2,11).


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

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

    Substitute here  m = 3,  a = 2,  b = 11,  and you will get

        y - 11 = 3*(x-2).

    It is the equation in the slope-point form.

    If you want to have it in the slope-intercept form, transform it in this way

        y = 3x - 6 + 11,   or

        y = 3x + 5.
</pre>

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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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