A "slope-intercept" form of a line is:

y = mx + b

where "m" is the slope and "b" gives the y-intercept.

a.parallel to the line 24x − 3y = 7 and passing through (−1, 4)

since the slopes of parallel lines are equal we will write 24x − 3y = 7 in slope intercept form

24x − 3y = 7

3y = 24x - 7 divide both sides by 3

y = 8x - 7

thus m = 8

now the only thing left to find is b

y = 8x + b goes trough (−1, 4) that is

4 = 8(-1) + b

b = 12

finally we have the slope-intercept equation of the wanted line:

y = 8x + 12

b.perpendicular to the line y = −(4/5)x − 7 and passing through (1, 6)

for perpendicular line the perpendicular slopes are negative reciprocals of each other

the slope of the line y = −(4/5)x − 7 is -4/5

negative reciprocal fo -4/5 is -(-4/5)^(-1) = 5/4 thus m = 5/4

now the only thing left to find is b

y = (5/4)x + b goes trough (1, 6) that is

6 = (5/4)*1 + b

b = 6 - 5/4

b = 19/4

finally we have the slope-intercept equation of the wanted line:

y = (5/4)x + 19/4