Part 1)
The slope-intercept form of the line equation

where m is the slope and b is the y-intercept
Given the equation

comparing with the slope-intercept form of the line equation y = 3x-4
Thus, the slope of the line: m = 3
We know that the parallel lines have the same slopes.
Thus, the slope of the paralellel line is also: 3
substituting the slope m = 3 and the point (5, -3) in the slope-intercept form

-3 = 3(5) + b
-3 = 15 + b
b = -3-15
b = -18
Therefore, the value of y-intercept b = -18
now substituting the slope m = 3 and the y-intercept b = -18 in the slope-intercept form

y = 3x + (-18)
y = 3x - 18
Therefore, the equation of line parallel to the given line
will be:

Part 2)
The slope-intercept form of the line equation

where m is the slope and b is the y-intercept
Given the equation

comparing with the slope-intercept form of the line equation y = 3x-4
Thus, the slope of the line: m = 3
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 3
Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3
substituting m = -1/3 and the point (5, -3) in the slope-intercept form




now substituting the slope m = -1/3 and the y-intercept b = -4/3 in the slope-intercept form



Therefore, the equation of the line perpendicular to the given line will be: