this question has two parts. first, answer part a. then, answer part b.\npart a\nwrite an equation in slope…

Explanation:

Part A

Step1: Determine the slope

Since parallel lines have the same slope. The slope of the line (y = 3x-5) is (m = 3).

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(4,-3)) and (m = 3). Substitute the values: (y-(-3)=3(x - 4)) (y + 3=3x-12)

Step3: Convert to slope - intercept form

Subtract 3 from both sides: (y=3x-12 - 3) (y=3x-15)

Part B

Step1: Determine the slope

Since perpendicular lines have slopes that are negative reciprocals. The slope of the line (y = 3x-5) is (m_1 = 3), so the slope of the perpendicular line (m_2=-\frac{1}{3})

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(4,-3)) and (m=-\frac{1}{3}) Substitute the values: (y-(-3)=-\frac{1}{3}(x - 4)) (y + 3=-\frac{1}{3}x+\frac{4}{3})

Step3: Convert to slope - intercept form

Subtract 3 from both sides: (y=-\frac{1}{3}x+\frac{4}{3}-3) (y=-\frac{1}{3}x+\frac{4 - 9}{3}) (y=-\frac{1}{3}x-\frac{5}{3})

Answer:

Part A: (y = 3x-15) Part B: (y=-\frac{1}{3}x-\frac{5}{3})