Consider the line =+8x5y−7.What is the slope of a line perpendicular to this line?What is the slope of a line parallel to this line?

To find the slope of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

Step 1: Rewrite the given line in slope-intercept form (y = mx + b), where m is the slope. The given line is 8x + 5y - 7 = 0. Rearranging the equation, we get 5y = -8x + 7. Dividing both sides by 5, we have y = (-8/5)x + 7/5.

Step 2: Identify the slope of the given line. Comparing the equation with the slope-intercept form, we see that the slope (m) of the given line is -8/5.

Step 3: Find the negative reciprocal of the slope. The negative reciprocal of -8/5 is 5/8.

Therefore, the slope of a line perpendicular to the given line is 5/8.

To find the slope of a line parallel to the given line, we can directly use the slope of the given line.

Therefore, the slope of a line parallel to the given line is also -8/5.