Question

consider the line 5x + 2y = 8. what is the slope of a line parallel to this line? what is the slope of a line perpendicular to this line? slope of a parallel line: slope of a perpendicular line:

Explanation:

Step1: Rewrite the line in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Given $5x + 2y=8$, solve for $y$:
$2y=-5x + 8$, so $y=-\frac{5}{2}x + 4$. The slope of the given line is $m =-\frac{5}{2}$.

Step2: Find the slope of a parallel line

Parallel lines have the same slope. So the slope of a line parallel to the given line is $-\frac{5}{2}$.

Step3: Find the slope of a perpendicular line

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. Let the slope of the perpendicular line be $m_2$. We know $m_1 =-\frac{5}{2}$, so $-\frac{5}{2}\times m_2=-1$. Solving for $m_2$, we get $m_2=\frac{2}{5}$.

Answer:

Slope of a parallel line: $-\frac{5}{2}$
Slope of a perpendicular line: $\frac{2}{5}$