Question
Drag the red and blue dots along the x-axis and y-axis to graph 4, x, plus, 7, y, equals, 204x+7y=20.
Answers
GPT-4o mini
To graph the equation \( 4x + 7y = 20 \), we can follow these steps to find points that satisfy the equation:
1. **Find x-intercept**: Set \( y = 0 \) in the equation.
\[
4x + 7(0) = 20 \implies 4x = 20 \implies x = 5
\]
So, the x-intercept is \( (5, 0) \).
2. **Find y-intercept**: Set \( x = 0 \) in the equation.
\[
4(0) + 7y = 20 \implies 7y = 20 \implies y = \frac{20}{7} \approx 2.857
\]
So, the y-intercept is \( (0, \frac{20}{7}) \) or approximately \( (0, 2.857) \).
3. **Plot the points**: You can now plot the points \( (5, 0) \) and \( (0, 2.857) \) on a graph.
4. **Draw the line**: Connect these points with a straight line, which represents the equation \( 4x + 7y = 20 \).
Now you can visualize the line on the graph by dragging the red dot to the x-intercept \( (5, 0) \) and the blue dot to the y-intercept \( (0, \frac{20}{7}) \). The line you draw through these points will be the graph of the equation.
1. **Find x-intercept**: Set \( y = 0 \) in the equation.
\[
4x + 7(0) = 20 \implies 4x = 20 \implies x = 5
\]
So, the x-intercept is \( (5, 0) \).
2. **Find y-intercept**: Set \( x = 0 \) in the equation.
\[
4(0) + 7y = 20 \implies 7y = 20 \implies y = \frac{20}{7} \approx 2.857
\]
So, the y-intercept is \( (0, \frac{20}{7}) \) or approximately \( (0, 2.857) \).
3. **Plot the points**: You can now plot the points \( (5, 0) \) and \( (0, 2.857) \) on a graph.
4. **Draw the line**: Connect these points with a straight line, which represents the equation \( 4x + 7y = 20 \).
Now you can visualize the line on the graph by dragging the red dot to the x-intercept \( (5, 0) \) and the blue dot to the y-intercept \( (0, \frac{20}{7}) \). The line you draw through these points will be the graph of the equation.