Various forms of the equation of a line

Correct answer: A. \((0,-2)\)

Every point on the \(y\)-axis has \(x=0\). Substituting this into the equation gives \(2(0)-5y=10\), so \(y=-2\). Therefore, the intersection point is \((0,-2)\). Option B has the wrong sign, while option C is the \(x\)-intercept. Exam tip: set \(x=0\) for the \(y\)-intercept and \(y=0\) for the \(x\)-intercept.

Correct answer: A. \((4,0)\)

Every point on the \(x\)-axis has \(y=0\). Substituting this into the equation gives \(5x+2(0)=20\), so \(x=4\), and the intersection point is \((4,0)\). Options B and D lie on the \(y\)-axis, while option C has the wrong sign for \(x\). Exam tip: To find the \(x\)-intercept, set \(y=0\).

Correct answer: A. It is parallel to the \(x\)-axis

In the equation \(y=-2\), the value of \(y\) remains fixed for every value of \(x\). Therefore, its graph is a horizontal line 2 units below the \(x\)-axis and is parallel to the \(x\)-axis. It does not pass through the origin because the origin has \(y\)-coordinate 0. Exam tip: the graph of \(y=c\) is always parallel to the \(x\)-axis, whereas the graph of \(x=c\) is parallel to the \(y\)-axis.