Question

Given XY: y = -x + 4 and P (8,5). Write the equation of a line perpendicular to XY and goes through point P.

y = 2x - 11
y = 2x - 21
y = 2x-3
y=-1/2 x - 11

Answer 1

To find the equation of a line perpendicular to XY and passing through point P (8,5), we need to determine the slope of XY and then find the negative reciprocal to get the slope of the perpendicular line. The equation of the line perpendicular is y = x - 3.

Step-by-step explanation:

To find the equation of a line perpendicular to XY and passing through point P (8,5), we need to determine the slope of XY and then find the negative reciprocal to get the slope of the perpendicular line. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The given equation XY: y = -x + 4 is already in this form, and the slope is -1. The negative reciprocal of -1 is 1, so the slope of the perpendicular line is 1.

Using the slope-intercept form and the coordinates of point P (8,5), we can substitute the values into the equation y = mx + b and solve for b. Plugging in the values, we get 5 = 1(8) + b. Solving for b, we find that b = -3.

Therefore, the equation of the line perpendicular to XY and passing through point P is y = x - 3.