# How to Graph an Equation in the Standard Form

Graphing an equation in standard form involves plotting the equation on a coordinate plane, where the $$x$$ and $$y$$-axes represent the horizontal and vertical dimensions, respectively. The standard form of an equation is $$Ax + By = C$$, where $$A, B,$$ and $$C$$ are constants.

## A step-by-step Guide to Graph an Equation in the Standard Form

Here are the steps to graph an equation in standard form:

### Step 1: Find the $$x$$ and $$y$$-intercepts

The $$x$$-intercept is the point where the equation intersects the $$x$$-axis, and the $$y$$-intercept is the point where the equation intersects the $$y$$-axis. To find the $$x$$-intercept, set $$y = 0$$ in the equation and solve for $$x$$. To find the $$y$$-intercept, set $$x = 0$$ in the equation and solve for $$y$$.

### Step 2: Plot the intercepts

Mark the $$x$$-intercept on the $$x$$-axis and the $$y$$-intercept on the $$y$$-axis. These two points will help you sketch the line.

### Step 3: Determine the slope

The slope of the line is the ratio of the change in $$y$$ to the change in $$x$$. Rearrange the equation in slope-intercept form $$(y = mx + b)$$, where $$m$$ is the slope and $$b$$ is the $$y$$-intercept. To find the slope, divide the coefficient of $$x$$ by the coefficient of $$y$$, and simplify if possible.

### Step 4: Plot additional points

To sketch the line, you need at least one additional point. Choose any value of $$x$$, plug it into the equation, and solve for $$y$$. This will give you the coordinates of another point on the line. Plot this point on the coordinate plane.

### Step 5: Sketch the line

Use a straight edge or ruler to draw a line through the intercepts and the additional point. This line represents the graph of the equation.

### Graph an Equation in the Standard Form – Examples 1

Graph the equation $$2x + 3y = 6$$

#### Solution:

Step 1: Find the intercepts.
To find the $$x$$-intercept, set $$y = 0: 2x + 3(0) = 6$$, so $$x = 3$$. The $$x$$-intercept is $$(3,0)$$.
To find the $$y$$-intercept, set $$x = 0: 2(0) + 3y = 6$$, so $$y = 2$$. The $$y$$-intercept is (0,2).

Step 2: Plot the intercepts.
Mark the $$x$$-intercept $$(3,0)$$ on the $$x$$-axis and the $$y$$-intercept $$(0,2)$$ on the $$y$$-axis.

Step 3: Determine the slope.
Rearrange the equation in slope-intercept form: $$3y = -2x + 6$$, so $$y = (-\frac{2}{3})x + 2$$. The slope is $$-\frac{2}{3}$$.

Choose any value of $$x$$, such as $$x =9$$, and solve for $$y: 2(9) + 3y = 6$$, so $$y = 0$$. The point $$(9,-4)$$ is on the line.

Step 5: Sketch the line.
Use a straight edge or ruler to draw a line through the intercepts and the additional point. The line represents the graph of the equation.

The graph of the equation $$2x + 3y = 6$$ is a straight line passing through the points $$(3,0)$$ and $$(0,2)$$.

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