Which of these ordered triples indicates where the plane cuts the y-axis for this equation 7x plus 2y plus 3z equals 42?

Answer 1

7x + 2y + 3z = 42

The plane intersects each coordinate plane, but since you are interested to know where the plane cuts y-axis, this will happen when the plane cuts xy-plane or yz-plane. So you can set z = 0, or x = 0.

So, set z = 0, then the plane will cuts the xy-plane along the line 7x + 2y = 42.

If x = 0, then the y-intercept is 42/2 = 21.