Find The Equation Of The Line (In Standard Form)Passing Through The Points (-3,4) And (5,1).

Find the equation of the line (in standard form)passing through the points (-3,4) and (5,1).

 

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\huge\rm{ANSWER:}

  • 3x + 8y = 23

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\huge\rm{SOLUTION:}

First, solve for the slope. Using the points (-3,4) and (5,1), we have

\rm{m = \frac{1 - 4}{5 - ( - 3)} = \frac{ - 3}{8}}

Substitute one of the given points and the value for slope in the equation y = mx+b, and solve for b. Using the point (-3,4), we have

\rm{4 = \frac{ - 3}{8} (- 3) + b}

\rm{32 = 9 + 8b}

\rm{8b = 23}

\rm{b = \frac{23}{8} }

Therefore, the equation of the line passing through (-3.4) and (5,1) is

\rm{y = \frac{ - 3}{8} x + \frac{23}{8}} \: or \: \rm{3x + 8y = 23}

To check, substitute the coordinates of the point (5,1) into the above equation.

\rm{3x + 8y - 23 = 0}

\rm{3(5) + 8(1) - 23 = 0}

\rm{15 + 8 - 23 = 0}

\rm{0 = 0}

Therefore, the equation 3x+8y=23 is indeed the required equation.

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\huge\rm{REMEMBER:}

\boxed{ \begin{array}{}{ \rm{The \: slope - intercept \: from \: of \: the} } \\ { \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{equation \: of \: a \: line \: is}} \\ { \rm{y= mx + b}} \\ { \rm{where \: m \: is \: the \: slope \: of \: the \: line}} \\ { \rm{\: and \: b \: is \: the \: y - intercept.}}\\ \end{array}}

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