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find an equation of the line passing through the pair points. write the equation in the form ax+by=c (-7,5),(-8,-9)

User Mjandrews
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Given the pair of coordinates;


\begin{gathered} (-7,5) \\ (-8,-9) \end{gathered}

We would begin by first calculating the slope of the line.

This is given by the formula;


m=(y_2-y_1)/(x_2-x_1)

The variables are as follows;


\begin{gathered} (x_1,y_1)=(-7,5) \\ (x_2,y_2)=(-8,-9) \end{gathered}

We will now substitute these into the formula for finding the slope as shown below;


\begin{gathered} m=((-9-5))/((-8-\lbrack-7)) \\ \end{gathered}
\begin{gathered} m=(-14)/(-8+7) \\ \end{gathered}
\begin{gathered} m=(-14)/(-1) \\ m=14 \end{gathered}

The slope of this line equals 14. We shall use this value along with a set of coordinates to now determine the y-intercept.

Using the slope-intercept form of the equation we would have;


y=mx+b

We would now substitute for the following variables;


\begin{gathered} m=14 \\ (x,y)=(-7,5) \end{gathered}
5=14(-7)+b
5=-98+b

Add 98 to both sides of the equation;


103=b

We now have the values of m, and b.The equation in "slope-intercept form" would be;


y=14x+103

To convert this linear equation into the standard form which is;


Ax+By=C

We would move the term with variable x to the left side of the equation;


\begin{gathered} y=14x+103 \\ \text{Subtract 14x from both sides;} \\ y-14x=103 \end{gathered}

We can now re-write and we'll have;


-14x+y=103

Note that the coefficients of x and y (that is A and B) are integers and A is positive;

Therefore, we would have;


\begin{gathered} \text{Multiply all through by -1} \\ 14x-y=-103 \end{gathered}

The equation of the line passing through the points given expressed in standard form is;

ANSWER:


14x-y=-103

User Wizardzeb
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