To find the slope of the line perpendicular to the given line equation $5x - 2y = 10$, follow these steps:

Step 1: Rearrange the equation into slope-intercept form $y = mx + b$

The given equation is: $5x - 2y = 10$ To get it into slope-intercept form $y = mx + b$, solve for $y$: $-2y = -5x + 10$ Divide by $-2$: $y = \frac{5}{2}x - 5$ Now the equation is in the form $y = mx + b$, where the slope $m = \frac{5}{2}$.

Step 2: Find the slope of the perpendicular line

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. The original slope is $\frac{5}{2}$, so the negative reciprocal is: $m_{\text{perpendicular}} = -\frac{2}{5}$

Step 3: Round to the nearest tenths place

$m_{\text{perpendicular}} = -0.4$

Thus, the slope of the line perpendicular to the given line is $-0.4$.

Would you like more details or have any questions? Here are some related questions for practice:

1. What is the slope of a line perpendicular to $2x + 3y = 9$?
2. How do you find the slope of a parallel line to $4x - 5y = 15$?
3. What is the equation of a line with slope $m = 2$ passing through the point $(1, -3)$?
4. How do you convert a line from standard form to slope-intercept form?
5. How do you find the equation of a line that is parallel to $y = 3x + 7$ and passes through $(4, 2)$?

Tip: For perpendicular slopes, always remember: flip the fraction and change the sign!