Answer:
y = -3x + 11
Step-by-step explanation:
To find the equation of the line perpendicular to [tex]y = \frac{1}{3}x - 2[/tex] and passing through the point (6, -7), we first need to determine the slope of the perpendicular line.
The given line has a slope of 1/3. As the slopes of perpendicular lines are negative reciprocals of each other, the slope of the perpendicular line is m = -3.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation to find its equation:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Point-slope form of a linear equation}}\\\\y-y_1=m(x-x_1)\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\textsf{ $(x_1,y_1)$ is a point on the line.}\end{array}}[/tex]
Substitute m = -3 and point (6, -7) into the equation and simplify:
[tex]y - (-7) = -3(x - 6)\\\\y + 7 = -3x + 18 \\\\y = -3x + 18 - 7 \\\\ y = -3x + 11[/tex]
Therefore, the equation of the line perpendicular to the given line and passing through the point (6, -7) is:
[tex]\Large\boxed{\boxed{y = -3x + 11}}[/tex]
