Question

question 14
8 pts
for the equation
6x - 4y = 24
the x-intercept is ( , )
and the y-intercept is ( , )

Explanation:

Step1: Find x-intercept

To find the x-intercept, set \( y = 0 \) in the equation \( 6x - 4y = 24 \).
Substituting \( y = 0 \), we get \( 6x - 4(0) = 24 \), which simplifies to \( 6x = 24 \).
Dividing both sides by 6, \( x = \frac{24}{6} = 4 \). So the x-intercept is \( (4, 0) \).

Step2: Find y-intercept

To find the y-intercept, set \( x = 0 \) in the equation \( 6x - 4y = 24 \).
Substituting \( x = 0 \), we get \( 6(0) - 4y = 24 \), which simplifies to \( -4y = 24 \).
Dividing both sides by -4, \( y = \frac{24}{-4} = -6 \). So the y-intercept is \( (0, -6) \).

Answer:

The x-intercept is \( (4, 0) \) and the y-intercept is \( (0, -6) \)