Answer:
y = -(1/3)x + 2
Step-by-step explanation:
A perpendicular line has a slope that is the negative inverse of the reference line. For a line with slope of 3, the perpendicular line would have a slope of -(1/3). That brings us to an equation of the slope-intercept form of:
y = -(1/3)x + b
Any equation having this form will be perpendicular to y = 3x + 4.
We could pick any value for b and the line will be perpendicular. The b value will only shift the graph up or down, not change the slope. But we are told that this line must go through point (3,1), so we need to pick a value of b that will make this happen.
To do this, enter the point (3,1) into the equation and solve for b:
y = -(1/3)x + b
1 = -(1/3)*3 + b
1 = -1 + b
b = 2
The equation of a line perpendicular to y = 3x + 4 that goes through point (3,1) is:
y = -(1/3)x + 2
See attached image.
