Question

fill in the blanks. for the line 2x + 3y = 6, the x - intercept is ___ and the y - intercept is ___. for the line 2x + 3y = 6, the x - intercept is \\(\square\\) and the y - intercept is \\(\square\\). (type integers or fractions.)

Explanation:

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

Substitute $y=0$ into $2x+3y=6$:
$2x + 3(0) = 6$

Step2: Solve for x

$2x = 6 \implies x = \frac{6}{2} = 3$

Step3: Find y-intercept (set x=0)

Substitute $x=0$ into $2x+3y=6$:
$2(0) + 3y = 6$

Step4: Solve for y

$3y = 6 \implies y = \frac{6}{3} = 2$

Answer:

The x-intercept is $3$ and the y-intercept is $2$.