Respuesta :
ANSWER
[tex]y\text{ = }\frac{5}{6}x\text{ + }\frac{31}{2}[/tex]EXPLANATION
We want to find the equation of the line that passes through (-9, 8) and is perpendicular to:
[tex]y\text{ = -}\frac{6}{5}x\text{ - 3}[/tex]The slope of a line perpendicular to another line is the negative inverse of the slope of the line it is perpendicular to.
The slope of the given line is -6/5.
This means that the slope of the line we need is:
[tex]\frac{5}{6}[/tex]Now, we can find the equation of the line by applying the point-slope method:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
m = slope of the line
Therefore, we have:
[tex]\begin{gathered} y\text{ - 8 = }\frac{5}{6}(x\text{ - (-9))} \\ y\text{ - 8 = }\frac{5}{6}(x\text{ + 9)} \\ y\text{ - 8 = }\frac{5}{6}x+(\frac{5}{6}\cdot\text{ 9)} \\ y\text{ - 8 = }\frac{5}{6}x\text{ +}\frac{15}{2} \\ y\text{ = }\frac{5}{6}x\text{ + }\frac{15}{2}\text{ + 8} \\ y\text{ = }\frac{5}{6}x\text{ + }\frac{31}{2} \end{gathered}[/tex]That is the equation of the line.
