· Perpendicular line have slopes that are opposite reciprocals of each other
· Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
The given equation is y = 3x + 4. The slope (m) of this line is 3. That means the slope of a line perpendicular is -1/3, rendering the equation for the line we're trying to find y = -1/3x + b. To find b (the y-intercept), plug the x- and y-values from the given coordinate into our above equation and solve.
The (x, y) coordinate: (9, -7)
y = -1/3x + b
-7 = -1/3(9) + b
-7 = -9/3 + b
-7 = -3 + b
-4 = b
b = -4
That is the y-intercept. The equation is complete.
Answer:
y = -1/3x - 4