Use intercepts to graph each equation. 6x-9y-18 = 0

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Rewrite the given equation in standard form: \(6x - 9y - 18 = 0\).

Find the x-intercept by setting \(y = 0\) in the equation and solving for \(x\). This means solving \(6x - 9(0) - 18 = 0\) for \(x\).

Find the y-intercept by setting \(x = 0\) in the equation and solving for \(y\). This means solving \(6(0) - 9y - 18 = 0\) for \(y\).

Plot the intercept points found on the coordinate plane: the x-intercept on the x-axis and the y-intercept on the y-axis.

Draw a straight line through the two intercept points to graph the equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Finding x-intercept

The x-intercept is the point where the graph crosses the x-axis, meaning y = 0. To find it, substitute y = 0 into the equation and solve for x. This gives a coordinate of the form (x, 0), which helps in plotting the graph.

Finding y-intercept

The y-intercept is the point where the graph crosses the y-axis, meaning x = 0. To find it, substitute x = 0 into the equation and solve for y. This results in a coordinate of the form (0, y), which is essential for graphing the line.

Graphing a linear equation using intercepts

Once the x- and y-intercepts are found, plot these points on the coordinate plane. Drawing a straight line through these two points represents the graph of the linear equation. This method is a straightforward way to graph lines without needing slope.

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