Respuesta :
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
The standard form for equation of the line is [tex]Ax + By = C \\[/tex]
We first find the slope of the line:
Slope, m is given by:
[tex]{\displaystyle {\Delta y\over \Delta x}={y_1-y_2\over x_1-x_2}}[/tex]
[tex]{\displaystyle m={-3-6\over 5-5}={-8\over 0}=\infty}[/tex]
This means that the slope is undefined.
And that the line is perpendicular to the x-axis and parallel to the y -axis.
Being that the line is parallel to the y-axis it means that the line intersect at no point with the y-axis so our equation is solved as follows:
Pick any point [tex](x,y)[/tex]along the line and one of the known points, say, [tex](5,6)[/tex]
So in solving for m,
we find that :
[tex]{\displaystyle {y_1-y_2\over x_1-x_2}={y-6\over x-5}={-8\over 0}}[/tex]
Cross multiplication gives us:
[tex]0(y-6)=-8(x-5)[/tex]
[tex]-8(x-5)=0[/tex]
Dividing through by [tex]-8[/tex] , we get:
[tex]x-5=0[/tex]
[tex]x=5[/tex]
