How to Find x- and y-intercepts in the Standard Form of Equation

The standard form of a linear equation in two variables is typically written as: \(Ax + By = C\), where \(A, B\), and \(C\) are constants and \(x\) and \(y\) are the variables. This form is sometimes also referred to as the “general form” or “standard linear form”.

A Step-by-step Guide to Find x- and y-intercepts in the Standard Form of Equation

In the standard form of the equation, it is not immediately clear what the \(x\)- and \(y\)-intercepts of the graph of the equation are. However, it is still possible to find them using algebraic techniques.

To find the \(x\)-intercept, we need to find the value of \(x\) when \(y = 0\). This means we can substitute \(0\) for y in the equation and solve for \(x\). The resulting value of \(x\) will be the \(x\)-intercept.

To find the \(y\)-intercept, we need to find the value of y when \(x = 0\). This means we can substitute \(0\) for \(x\) in the equation and solve for \(y\). The resulting value of \(y\) will be the \(y\)-intercept.

Finding x- and y-intercepts in the Standard Form of Equation – Examples 1

Find the x- and y-intercepts of the line \(2x + 3y = 6\)

Solution:

To find the \(x\)-intercept, we set \(y = 0\) and solve for \(x\):

\(2x + 3(0) = 6\)

\(2x = 6\)

\(x = 3\)

So the \(x\)-intercept is \((3, 0)\).

To find the \(y\)-intercept, we set \(x = 0\) and solve for \(y\):

\(2(0) + 3y = 6\)

\(3y = 6\)

\(y = 2\)

So the \(y\)-intercept is \((0, 2)\).

Therefore, the graph of the equation \(2x + 3y = 6\) intersects the \(x\)-axis at \((3, 0)\) and the \(y\)-axis at \((0, 2)\).