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 \(y\):

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

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\(3y = 6\)

\(y = 2\)

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 \((0, 2)\).

Exercises for Finding \(x\)- and \(y\)-intercepts in the Standard Form of Equation

Find the \(x\)- and \(y\)-intercepts of each line.

1. \(\color{blue}{2x+y=-4}\)
2. \(\color{blue}{x-y=6}\)
3. \(\color{blue}{3x-2y=18}\)

1. \(\color{blue}{\left(-2,\:0\right), \left(0,\:-4\right)}\)
2. \(\color{blue}{\left(6,\:0\right), \left(0,\:-6\right)}\)
3. \(\color{blue}{\left(6,\:0\right), \left(0,\:-9\right)}\)