Question

consider the following equation. \\(9y + 2x = 2(9 + x)\\) step 2 of 2: graph the equation by plotting the \\(x\\)- and \\(y\\)-intercepts. if an intercept does not exist, or is duplicated, use another point on the line to plot the graph. answer 2 points points can be moved by dragging or using the arrow keys. any lines or curves will be drawn once all required points are plotted and will update whenever a point is moved. keypad keyboard shortcuts enable zoom/pan

Explanation:

Step1: Simplify the given equation

First, expand and simplify the right-hand side:
$$9y + 2x = 2(9 + x)$$
$$9y + 2x = 18 + 2x$$
Subtract $2x$ from both sides:
$$9y = 18$$
$$y = 2$$

Step2: Find x-intercept

The x-intercept occurs where $y=0$. Substitute $y=0$ into $y=2$:
$0=2$, which is false. So no x-intercept exists.

Step3: Find y-intercept

The y-intercept occurs where $x=0$. Substitute $x=0$ into $y=2$:
The line $y=2$ intersects the y-axis at $(0, 2)$.

Step4: Choose a second point

Since $y=2$ for all $x$, pick any $x$-value, e.g., $x=3$. The point is $(3, 2)$.

Answer:

• No x-intercept exists.
• Y-intercept: $(0, 2)$
• Second point on the line: $(3, 2)$

The graph is a horizontal line at $y=2$ passing through these points.