https://file.aiquickdraw.com/mathbot/file/17279572864486b8tzrpq.jpg

To solve the equation \(4x + 2y = 20\) and correctly graph it, we can first find the intercepts with the x-axis and y-axis. These intercepts are where the graph crosses the axes and help determine the correct placement of the red and blue dots.

### Step 1: Find the x-intercept
The x-intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation:

\[
4x + 2(0) = 20 \implies 4x = 20 \implies x = \frac{20}{4} = 5.
\]

So, the x-intercept is at \(x = 5\), or the point \((5, 0)\).

### Step 2: Find the y-intercept
The y-intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation:

\[
4(0) + 2y = 20 \implies 2y = 20 \implies y = \frac{20}{2} = 10.
\]

So, the y-intercept is at \(y = 10\), or the point \((0, 10)\).

### Graphing the Line:
1. The red dot should be placed at the x-intercept \((5, 0)\).
2. The blue dot should be placed at the y-intercept \((0, 10)\).

However, based on the graph in the image:
- The red dot is placed at approximately \(x = 7\), but it should be at \(x = 5\).
- The blue dot is placed at \(y = 5\), but it should be at \(y = 10\).

To correct the graph, the red and blue dots need to be repositioned as follows:
- Move the red dot to \( (5, 0) \).
- Move the blue dot to \( (0, 10) \).

Would you like any further explanation, or do you have any specific questions on how this was done?

Here are five related questions to expand your understanding:
1. How do you find the slope of the line from the equation \(4x + 2y = 20\)?
2. Can this equation be rewritten in slope-intercept form? How?
3. What would the graph look like if the equation was \(4x - 2y = 20\)?
4. How does changing the coefficients of \(x\) and \(y\) affect the graph of the equation?
5. What is the general process for graphing any linear equation?

**Tip:** When graphing a line, finding the x- and y-intercepts is a quick way to establish two points, which is enough to draw the line.

Drag the red and blue dots along the x-axis and y-axis to graph 4x + 2y = 20.

Learn how to graph the linear equation 4x + 2y = 20 by finding the x and y intercepts and placing points on the coordinate plane. Understand key concepts such as slope and intercepts with detailed explanations. Suitable for Grades 8-10.

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