Slope Intercept Form of a line is y = mx + b, where m = slope, b = y - intercept, and x and y are variables.
To write the equation of a line in slope intercept form, we need to find m and b first.
Parallel lines have equal slopes.
Perpendicular lines have slopes that are negative reciprocals.
y = 3x + 5 is a line with a slope of m = 3.
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, - 8) = (x, y).
To write the equation in slope intercept form, y = mx + b, we also need to find the y - intercept, which is b.
y = mx + b
-8 = (-1/3)(6) + b (we've set up the equation with only one unknown, b, that we can now solve for)
-8 = -2 + b
b = -6
With a slope, m = -1/3, and a y-intercept, b = -6, the equation of our line relating x and y is:
y = (-1/3)x - 6
