Questions: What is the slope of a line parallel to -2 x+5 y=8 ? a. 2/5 b. -2/5 c. -4 d. -2

What is the slope of a line parallel to -2 x+5 y=8 ? a. 2/5 b. -2/5 c. -4 d. -2
Transcript text: 2. What is the slope of a line parallel to $-2 x+5 y=8 ?$ a. $\frac{2}{5}$ b. $-\frac{2}{5}$ C. -4 d. -2
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Solution

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Solution Steps

To find the slope of a line parallel to the given line, we first need to convert the given equation into slope-intercept form (y = mx + b), where m is the slope. The slope of the parallel line will be the same as the slope of the given line.

Solution Approach
  1. Convert the given equation \(-2x + 5y = 8\) into slope-intercept form.
  2. Identify the slope (m) from the slope-intercept form.
  3. The slope of the parallel line will be the same as the slope of the given line.
Step 1: Convert to Slope-Intercept Form

We start with the equation of the line given by

\[ -2x + 5y = 8. \]

To convert this into slope-intercept form \(y = mx + b\), we solve for \(y\):

\[ 5y = 2x + 8 \implies y = \frac{2}{5}x + \frac{8}{5}. \]

Step 2: Identify the Slope

From the slope-intercept form \(y = \frac{2}{5}x + \frac{8}{5}\), we can identify the slope \(m\) of the line as

\[ m = \frac{2}{5}. \]

Step 3: Determine the Slope of the Parallel Line

Since parallel lines have the same slope, the slope of a line parallel to the given line is also

\[ m_{\text{parallel}} = \frac{2}{5}. \]

Final Answer

The slope of a line parallel to the given line is

\[ \boxed{\frac{2}{5}}. \]

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