Question

find the x and y intercepts of this linear equation. 6x - 9y = 54 x-intercept (?, ) y-intercept (, )

Explanation:

Step1: Find x-intercept, set $y=0$

Substitute $y=0$ into $6x - 9y = 54$:
$6x - 9(0) = 54$
$6x = 54$

Step2: Solve for x

$x = \frac{54}{6} = 9$
So x-intercept is $(9, 0)$

Step3: Find y-intercept, set $x=0$

Substitute $x=0$ into $6x - 9y = 54$:
$6(0) - 9y = 54$
$-9y = 54$

Step4: Solve for y

$y = \frac{54}{-9} = -6$
So y-intercept is $(0, -6)$

Answer:

x-intercept: $(9, 0)$
y-intercept: $(0, -6)$