Final answer:
The equation of line n, which is parallel to line m and passes through the point (4, -3), is y = (3/2)x - 9. To find this, we used the fact that parallels have equal slopes, and the slope of line m, being perpendicular to a line with slope -2/3, is the negative reciprocal, which is 3/2. Then we used the slope-intercept form, y = mx + b, to solve for the y-intercept given the point (4, -3).
Step-by-step explanation:
The subject of this question is finding the equation of line n that is parallel to line m. Since line m is perpendicular to a line with slope -2/3, its slope is the negative reciprocal of -2/3, which is 3/2. Therefore, line n will also have a slope of 3/2 because it is parallel to line m. To find the y-intercept of line n, we use the point it passes through, (4, -3), and the slope 3/2.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Starting with the slope-intercept equation, plug in the slope (3/2) and the point (4, -3):
y = (3/2)x + b
-3 = (3/2)(4) + b
-3 = 6 + b
b = -3 - 6
b = -9
So the equation of line n is y = (3/2)x - 9 in slope-intercept form.