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.