Step-by-step Solution:

The given equation of the straight line is: \[ y = -x + 6 \] The slope-intercept form of a line is: \[ y = mx + c \] where \( m \) is the slope. Comparing, we get the slope of the given line as \( m = -1 \). A line is parallel to the given line if it has the same slope \( m = -1 \). Checking the given options: # Option A: \( 2y + 3x = -5 \) Rearrange in slope-intercept form: \[ 2y = -3x - 5 \] \[ y = -\frac{3}{2}x - \frac{5}{2} \] Here, the slope is \( -\frac{3}{2} \neq -1 \), so this line is not parallel. # Option B: \( -3x - 3y + 7 = 0 \) Rearrange in slope-intercept form: \[ -3y = 3x - 7 \] \[ y = -x + \frac{7}{3} \] Here, the slope is \( -1 \), so this line is parallel. # Option C: \( 2y = -2x + 12 \) Rearrange in slope-intercept form: \[ y = -x + 6 \] Here, the slope is \( -1 \), so this line is parallel. # Option D: \( y - x = \frac{1}{10} \) Rearrange in slope-intercept form: \[ y = x + \frac{1}{10} \] Here, the slope is \( 1 \neq -1 \), so this line is not parallel. Conclusion: Lines in Option B and Option C are parallel to the given line. Hence, the correct answer is: \[ \text{E. B and C are correct.} \]