find the slope line perpendicular  to the lines whose  equation is 5x-2y=10 fully  simplify your answer ROUND TO THE NEAREST TENTHS PLACE1

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!

find the slope line perpendicular to the lines whose equation is 5x - 2y = 10 fully simplify your answer ROUND TO THE NEAREST TENTHS PLACE

Learn how to find the slope of a line perpendicular to 5x - 2y = 10. This step-by-step guide explains how to convert the equation into slope-intercept form, calculate the perpendicular slope, and round to the nearest tenth. Suitable for Grades 8-10.

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