Question

1. find the x-intercept and y-intercept of the equation 3x + 6y = 24.

Explanation:

Step1: Find x-intercept (set y=0)

To find the x - intercept, we set \( y = 0 \) in the equation \( 3x+6y = 24 \). Substituting \( y = 0 \) gives us \( 3x+6(0)=24 \), which simplifies to \( 3x=24 \). Then, we solve for \( x \) by dividing both sides of the equation by 3: \( x=\frac{24}{3}=8 \). So the x - intercept is at the point \( (8,0) \).

Step2: Find y-intercept (set x=0)

To find the y - intercept, we set \( x = 0 \) in the equation \( 3x+6y = 24 \). Substituting \( x = 0 \) gives us \( 3(0)+6y=24 \), which simplifies to \( 6y = 24 \). Then, we solve for \( y \) by dividing both sides of the equation by 6: \( y=\frac{24}{6} = 4 \). So the y - intercept is at the point \( (0,4) \).

Answer:

The x - intercept is \( (8,0) \) and the y - intercept is \( (0,4) \)