The equation of a straight line ,l1 is 2y+8x-10.another line,l2 cuts l1 at right angles such that the point of intersection of the two lines has coordinates(-3,k).find the equation of l2 and the value of k
We can begin by finding the slope of the first line, l1. To do this, we can rearrange the equation into slope-intercept form:
2y + 8x - 10 = 0
2y = -8x + 10
y = -4x + 5
So the slope of l1 is -4. Since l2 intersects l1 at right angles, its slope will be the negative reciprocal of -4, which is 1/4.
We also know that the point (-3, k) is on l2. Using the point-slope form of a line equation, we can plug in the slope and point to get the equation of l2:
y - k = (1/4)(x + 3)
To find k, we can plug in the coordinates of (-3,k):
k - k = (1/4)(-3 + 3)
0 = 0
So k can be any value, and the equation of l2 is simply:
y - k = (1/4)(x + 3)