Question

find the x - and y - intercepts of the graph of (2x - 5y = 6). state each answer as an integer or an improper fraction in simplest form.
answer
attempt 1 out of 100
x - intercept:

y - intercept:

Explanation:

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

To find the x - intercept, we set \( y = 0 \) in the equation \( 2x-5y = 6 \). Substituting \( y = 0 \) gives us \( 2x-5(0)=6 \), which simplifies to \( 2x=6 \). Then, we solve for \( x \) by dividing both sides of the equation by 2: \( x=\frac{6}{2}=3 \).

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

To find the y - intercept, we set \( x = 0 \) in the equation \( 2x - 5y=6 \). Substituting \( x = 0 \) gives us \( 2(0)-5y=6 \), which simplifies to \( - 5y=6 \). Then, we solve for \( y \) by dividing both sides of the equation by - 5: \( y=\frac{6}{-5}=-\frac{6}{5} \).

Answer:

x - intercept: \( 3 \)
y - intercept: \( -\frac{6}{5} \)