Respuesta :
Given the pair of coordinates;
[tex]\begin{gathered} (-7,5) \\ (-8,-9) \end{gathered}[/tex]We would begin by first calculating the slope of the line.
This is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are as follows;
[tex]\begin{gathered} (x_1,y_1)=(-7,5) \\ (x_2,y_2)=(-8,-9) \end{gathered}[/tex]We will now substitute these into the formula for finding the slope as shown below;
[tex]\begin{gathered} m=\frac{(-9-5)}{(-8-\lbrack-7)} \\ \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-14}{-8+7} \\ \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-14}{-1} \\ m=14 \end{gathered}[/tex]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;
[tex]y=mx+b[/tex]We would now substitute for the following variables;
[tex]\begin{gathered} m=14 \\ (x,y)=(-7,5) \end{gathered}[/tex][tex]5=14(-7)+b[/tex][tex]5=-98+b[/tex]Add 98 to both sides of the equation;
[tex]103=b[/tex]We now have the values of m, and b.The equation in "slope-intercept form" would be;
[tex]y=14x+103[/tex]To convert this linear equation into the standard form which is;
[tex]Ax+By=C[/tex]We would move the term with variable x to the left side of the equation;
[tex]\begin{gathered} y=14x+103 \\ \text{Subtract 14x from both sides;} \\ y-14x=103 \end{gathered}[/tex]We can now re-write and we'll have;
[tex]-14x+y=103[/tex]Note that the coefficients of x and y (that is A and B) are integers and A is positive;
Therefore, we would have;
[tex]\begin{gathered} \text{Multiply all through by -1} \\ 14x-y=-103 \end{gathered}[/tex]The equation of the line passing through the points given expressed in standard form is;
ANSWER:
[tex]14x-y=-103[/tex]