Question
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Simplify the equation if possible. Find the x-intercept and the \( y \)-intercept. Then graph the equation. \( -2 x-9 y=9 \)

Ask by Cole Lynch. in the United States
Mar 13,2025

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Tutor-Verified Answer

Answer

To graph the equation \( -2x - 9y = 9 \), find the x-intercept and y-intercept. The x-intercept is \( x = -\frac{9}{2} \) and the y-intercept is \( y = -1 \). Plot these points and draw a line through them to graph the equation.

Solution

Find the x-intercept and y-intercept of the equation \( -2x-9y=9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-2x-9y=9\) - step1: Move the expression to the right side: \(-2x=9+9y\) - step2: Change the signs: \(2x=-9-9y\) - step3: Divide both sides: \(\frac{2x}{2}=\frac{-9-9y}{2}\) - step4: Divide the numbers: \(x=-\frac{9+9y}{2}\) Find the x-intercept and y-intercept of the equation \( -2x-9y=9 \). Solve the equation by following steps: - step0: Solve for \(y\): \(-2x-9y=9\) - step1: Move the expression to the right side: \(-9y=9+2x\) - step2: Change the signs: \(9y=-9-2x\) - step3: Divide both sides: \(\frac{9y}{9}=\frac{-9-2x}{9}\) - step4: Divide the numbers: \(y=-\frac{9+2x}{9}\) The x-intercept of the equation \( -2x-9y=9 \) is \( x = -\frac{9+9y}{2} \) and the y-intercept is \( y = -\frac{9+2x}{9} \). To graph the equation, we can plot the x-intercept and y-intercept on a coordinate plane and then draw a line through them. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Let's plot the x-intercept and y-intercept on a coordinate plane and then draw a line through them to graph the equation.

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Simplify this solution

The Deep Dive

To simplify the equation, we can rewrite it in slope-intercept form \( y = mx + b \). Starting with \( -2x - 9y = 9 \), we can isolate \( y \): \[ -9y = 2x + 9 \] \[ y = -\frac{2}{9}x - 1 \] Now, for the x-intercept, we set \( y = 0 \): \[ 0 = -\frac{2}{9}x - 1 \implies \frac{2}{9}x = -1 \implies x = -\frac{9}{2} = -4.5 \] For the y-intercept, we set \( x = 0 \): \[ y = -\frac{2}{9}(0) - 1 = -1 \] So, the x-intercept is \((-4.5, 0)\) and the y-intercept is \((0, -1)\). To graph the equation, plot these intercepts and draw a straight line through them. For some fun facts, did you know that intercepts can help you quickly sketch a graph without needing to plot multiple points? Just grab those intercepts and connect the dots! Also, keep in mind that slopes like the one from this equation represent the steepness of the line – here, it’s negative! So you're looking at a descending line that goes down from left to right, adding flair to your graphing skills!

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