Answer:
y = -1/3x + 2
Explanation:
The gradient of the given line is 3 because (y = mx +c where m is the gradient)
Therefore, to find the gradient of the perpendicular line (at 90 degrees), you need to find the negative reciprocal.
The negative reciprocal of 3 is -1/3 because imagine if 3 = 3/1, to get the reciprocal, you flip it, and to get the negative, you just flip the sign.
Now we know that Line M is y = -1/3x + c, we need to find the y-intercept.
To do this, just input the point (3,1) into y = -1/3x + c, to get c. This is because we know (3,1) is on the line from the question.
So it would be 1 = (-1/3 x 3) +c
Which would be 1 = -1 +c
And so c = 2
Put everything together and you get y = -1/3x + 2