In order to determine the equation with a line perpendicular to the given equation, consider that for two perpendicular lines, the relation in between their slopes is:
m1 = -1/(m2)
where m1 and m2 are the slopes of the lines.
Write the given equation in slope-intercept form to identify the slope m1, as follow:
7x + 3y = -18 subtract 7x both sides
3y = - 7x - 18 divide by 3 both sides
y = -7/3 x - 6
remind that the general form of the equation of a line can be written as follow:
y = mx + b
where m is the slope. Based on the expression for y = -7/3 x - 6, you have
m1 = -7/3
then, calculate m2:
m2 = -1/(m1)
m2 = -1/(-7/3)
m2 = 3/7
Hence, it is necessary that the perpendicular line has a positive slope of 3/7.
Fromt the given answer choices, you can notice that the only option with the required slope is:
y = 3/7 x + 5