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

In this comprehensive and step-by-step guide, you will learn how to find x- and y-intercepts when the standard form of equations is provided. 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 $$(0, 2)$$.

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