Question

Find the line that is perpendicular to line (n) that passes through point (2, -3). If the slope of the perpendicular line is (2/5), what is the y-intercept of the perpendicular line?

a) (b = 19/5)
b) (b = 11/5)
c) (b = 4)
d) (b = 2)

Answer 1

To find the y-intercept of the perpendicular line, the slope-intercept form y = mx + b is used with the known values. The correct y-intercept, after solving the equation with the provided point and slope, is b = 19/5, corresponding to option a).

Step-by-step explanation:

The student is asking for the y-intercept of a line perpendicular to line (n) and passing through the point (2, -3) with a given slope of 2/5. To find the y-intercept, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the known coordinates (2, -3) for x and y, and 2/5 for m, we get -3 = (2/5)(2) + b. Simplifying this, we have -3 = 4/5 + b, and solving for b, we find that b = -3 - 4/5, which simplifies to -15/5 - 4/5 = -19/5. Therefore, the correct y-intercept of the perpendicular line is b = 19/5, which corresponds to option a).