Line M passes through point (3,1) and is perpendicular to the line of the equation y=3x+4. Which equation describes the graph of M? A) y=-3x+16
B) y=-1/3x+2
C)y=-1/3x+4
D)y=1/3x+6

y = -1/3x + 2

Step-by-step 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

the answer is b.)

< 1=< 2