Consider the line =−3x4y−4.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. Given line: -3x + 4y - 4 = 0 Rearranging the equation, we get: 4y = 3x + 4 Dividing both sides by 4, we get: y = (3/4)x + 1

Step 2: Determine the slope of the given line. Comparing the equation with the slope-intercept form, we see that the slope (m) is 3/4.

Step 3: Find the negative reciprocal of the slope. The negative reciprocal of 3/4 is -4/3.

Therefore, the slope of a line perpendicular to the given line is -4/3.

To find the slope of a line parallel to the given line, we need to find the slope of the given line.

Step 1: Determine the slope of the given line. From the previous steps, we found that the slope of the given line is 3/4.

Therefore, the slope of a line parallel to the given line is also 3/4.