i) Determine if the line \( -2 x+5 y=10 \) is parallel to the line \( y=\frac{2}{5} x+8 \) no yes

To determine if the lines are parallel, we need to compare their slopes. 1. **Find the slope of the first line**: The equation of the first line is given in standard form: \[ -2x + 5y = 10 \] We can convert it to slope-intercept form \(y = mx + b\) by solving for \(y\): \[ 5y = 2x + 10 \] \[ y = \frac{2}{5}x + 2 \] The slope \(m_1\) of the first line is \(\frac{2}{5}\). 2. **Find the slope of the second line**: The second line is already in slope-intercept form: \[ y = \frac{2}{5}x + 8 \] The slope \(m_2\) of the second line is also \(\frac{2}{5}\). 3. **Compare the slopes**: Since both lines have the same slope \(m_1 = m_2 = \frac{2}{5}\), the lines are parallel. Thus, the answer is **yes**, the line \( -2x + 5y = 10 \) is parallel to the line \( y = \frac{2}{5}x + 8 \).