Various forms of the equation of a line

Correct answer: A. \\(x=2\\)

A point on the \\(x\\)-axis has a \\(y\\)-coordinate of zero. Thus, \\(3x-6=0\\), which gives \\(3x=6\\) and hence \\(x=2\\). Therefore, option A is correct. Remember that \\(3\\) is the slope of the line; to find the \\(x\\)-intercept, set \\(y=0\\).

Correct answer: A. \((0,8)\)

Every point on the \(y\)-axis has \(x=0\). Substituting this into the equation gives \(2(0)+y=8\), so \(y=8\) and the intersection point is \((0,8)\). The point \((8,0)\) is the \(x\)-intercept. Exam tip: To find a \(y\)-intercept, set \(x=0\).

Correct answer: A. \(x=\frac{9}{2}\)

Every point on the x-axis has \(y=0\). Substituting this in the equation gives \(2x-3(0)=9\), so \(2x=9\) and \(x=\frac{9}{2}\). Therefore, the intercept point is \(\left(\frac{9}{2},0\right)\). Exam tip: set \(y=0\) to find an x-intercept and set \(x=0\) to find a y-intercept.

Correct answer: B. (3,-3)

For the point \((3,-3)\), \(x=3\) and \(y=-3\), so it satisfies \(y=-x\). In option A, when \(x=3\), the value of \(y\) should be \(-3\), not \(3\), so it is incorrect. As an exam tip, substitute the coordinates directly into the equation; every point on this line satisfies \(x+y=0\).