5. write an equation for the line that contains point (-5, 6) and is perpendicular to the line y = 5/3x + 2

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line $y = \frac{5}{3}x+2$ is $m_1=\frac{5}{3}$. For two - perpendicular lines with slopes $m_1$ and $m_2$, $m_1\times m_2=- 1$. So, $\frac{5}{3}m_2=-1$, then $m_2 =-\frac{3}{5}$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-5,6)$ and $m =-\frac{3}{5}$. Substitute these values into the formula: $y - 6=-\frac{3}{5}(x + 5)$.

Step3: Simplify the equation

Expand the right - hand side: $y-6=-\frac{3}{5}x-3$. Then add 6 to both sides to get the slope - intercept form: $y=-\frac{3}{5}x + 3$.

Answer:

$y=-\frac{3}{5}x + 3$