Drag the red and blue dots along the x-axis and y-axis to graph 5, x, plus, 10, y, equals, 305x+10y=30.

To graph the equation \( 305x + 10y = 30 \), we need to transform it into a more familiar form for graphing, such as the slope-intercept form or the intercepts form. Here's how we can approach this step-by-step:

### Step 1: Simplify the equation
Divide the entire equation by 5 to make the coefficients smaller and easier to handle:
\[
305x + 10y = 30
\]
Dividing by 5 gives:
\[
61x + 2y = 6
\]

### Step 2: Solve for the intercepts
We can find the intercepts by setting \( x = 0 \) to find the \( y \)-intercept, and \( y = 0 \) to find the \( x \)-intercept.

- **For the \( y \)-intercept**, set \( x = 0 \):
\[
61(0) + 2y = 6 \quad \Rightarrow \quad 2y = 6 \quad \Rightarrow \quad y = 3
\]
So, the \( y \)-intercept is \( (0, 3) \).

- **For the \( x \)-intercept**, set \( y = 0 \):
\[
61x + 2(0) = 6 \quad \Rightarrow \quad 61x = 6 \quad \Rightarrow \quad x = \frac{6}{61}
\]
So, the \( x \)-intercept is \( \left(\frac{6}{61}, 0\right) \).

### Step 3: Plot the points
- The \( y \)-intercept is \( (0, 3) \).
- The \( x \)-intercept is approximately \( \left(0.098, 0\right) \), which is very close to zero.

### Step 4: Draw the line
Now, you can drag the red and blue dots to plot these intercepts on the coordinate plane, then connect them with a straight line to represent the equation \( 61x + 2y = 6 \).

Would you like more details or have any questions?

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Here are 5 relative questions:
1. How do you find the slope of the line from this equation?
2. What does the small \( x \)-intercept value signify in this context?
3. How do we handle larger coefficients in equations while graphing?
4. Can you express the equation in slope-intercept form?
5. What happens to the graph if the constant on the right-hand side changes?

**Tip:** When graphing, always start with the intercepts if you're unsure of the slope!

Drag the red and blue dots along the x-axis and y-axis to graph 305x + 10y = 30.

Learn how to graph the linear equation 305x + 10y = 30 using intercepts. This problem demonstrates finding the x- and y-intercepts, simplifying the equation, and graphing it on a coordinate plane. Suitable for students in Grades 9-11.

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