Various forms of the equation of a line

Correct answer: B. y-axis

The equation \(x=0\) means that the x-coordinate of every point on the line is zero, while the y-coordinate can have any value. All such points lie on the y-axis, so the correct answer is the y-axis. Exam tip: the equation of the x-axis is \(y=0\).

Correct answer: A. 5

In the standard form \(y=mx+c\), the \(y\)-intercept is \(c\), since putting \(x=0\) gives \(y=c\). Here, \(c=5\), so the \(y\)-intercept is 5 and the point is \((0,5)\). The value \(-3\) is the slope, not the intercept. Exam tip: For any point on the \(y\)-axis, substitute \(x=0\).

Correct answer: B. Vertical line

In \(x=-2\), the x-coordinate is fixed at -2 while y can be any real number. The points \((-2,y)\) form a vertical line, parallel to the y-axis.

Correct answer: B. (3, 4)

The governing idea is that a point at the intersection of two lines must satisfy both equations simultaneously. The first line fixes the x-coordinate at 3. Substitute x = 3 into the second equation: 3 + 2y = 11. Subtracting 3 gives 2y = 8, and division by 2 gives y = 4. Thus the common point is (3, 4), so option B is correct. A frequent error is to interchange the coordinates and choose (4, 3), but x = 3 rules that out immediately. Option C has the correct x-coordinate but fails because 3 + 2(2) = 7, not 11. Option D also fails the vertical-line condition because its x-coordinate is 5. Substitution into both original equations is the reliable verification method.