ANSWER and EXPLANATION
We want to find the line that is perpendicular to the given equation and passes through (2, 3).
The given equation is -(1/3)x + 5
The slope of any line perpendicular to another line is the negative inverse of the slope of that line.
The slope of the equation is -1/3.
Therefore, the slope of the line we are looking for is:
[tex]\begin{gathered} \frac{-1}{\frac{-1}{3}}\text{ = -1 }\cdot\text{ -}3 \\ =\text{ 3} \end{gathered}[/tex]
We can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
This means that the equation of the line is:
y - 3 = 3(x - 2)
This is the equation in point-slope form
Simplifying:
y - 3 = 3x - 6
y = 3x - 6 + 3
y = 3x - 3
That is the equation of the line in Slope Intercept form.
