Question

drag the red and blue dots along the x-axis and y-axis to graph $x - 10y = 5$.

Explanation:

Step1: Find x-intercept (y=0)

Substitute \( y = 0 \) into \( x - 10y = 5 \):
\( x - 10(0) = 5 \)
\( x = 5 \). So x-intercept is \( (5, 0) \).

Step2: Find y-intercept (x=0)

Substitute \( x = 0 \) into \( x - 10y = 5 \):
\( 0 - 10y = 5 \)
\( -10y = 5 \)
\( y = \frac{5}{-10} = -0.5 \). Wait, the blue dot in the graph is at \( (0, 5) \), which is incorrect. Let's recalculate. Wait, maybe I made a mistake. Wait, the equation is \( x - 10y = 5 \). Let's solve for y: \( -10y = 5 - x \) → \( y = \frac{x - 5}{10} = \frac{1}{10}x - \frac{1}{2} \). So y-intercept is when x=0: \( y = -\frac{1}{2} = -0.5 \). But the graph's blue dot is at (0,5), which is wrong. Wait, maybe the original graph is incorrect, but we need to find the correct intercepts. Wait, the red dot is at (5,0), which matches the x-intercept (5,0). For the y-intercept, when x=0, y= (0 -5)/10 = -0.5. So the blue dot should be at (0, -0.5), but the graph has it at (0,5). So to graph correctly, drag the red dot to (5, 0) (which it seems to be, but check) and blue dot to (0, -0.5). Wait, maybe the problem is to adjust the dots to the correct intercepts. So the correct x-intercept is (5,0) (red dot) and y-intercept is (0, -0.5) (blue dot). But the current blue dot is at (0,5), which is wrong. So we need to move the blue dot down to (0, -0.5) and red dot to (5,0) (which is already there? Wait, the red dot is at x=5, y=0, which is correct. The blue dot is at (0,5), which is wrong. So solve for y when x=0: \( 0 -10y =5 \) → y= -0.5. So the blue dot should be at (0, -0.5), and red at (5,0).

Answer:

To graph \( x - 10y = 5 \):

• Red dot (x-intercept): Drag to \( (5, 0) \) (already at x=5, y=0, correct).
• Blue dot (y-intercept): Drag to \( (0, -0.5) \) (current blue dot at (0,5) is incorrect; solve \( x=0 \) in \( x - 10y =5 \) to get \( y = -0.5 \)).