Question

consider the point (8,2) and the Line L, given by the equation y=4x-6. what is the equation of the line in slope intercept form passing through point p and perpendicular to Line L

Answer 1

Answer: y = -x/4 + 4

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 4x - 6

Comparing with the slope intercept form, slope = 4

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of line L passing through (8,2) is - 1/4

To determine the intercept, we would substitute m = - 1/4, x = 8 and y = 2 into y = mx + c. It becomes

2 = - 1/4 × 8 + c

2 = - 2 + c

c = 2 + 2 = 4

The equation becomes

y = -x/4 + 4