Answer:
[tex]\huge\boxed{x-intercept=-\dfrac{14}{3}=-4\dfrac{2}{3}}\\\boxed{y-intercept=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
Step-by-step explanation:
[tex]-3x+9y=14\\\\x-intercept\ \text{for}\ y=0:\\\\-3x+9(0)=14\\-3x+0=14\\-3x=14\qquad\text{divide both sides by (-3)}\\\boxed{x=-\dfrac{14}{3}=-4\dfrac{2}{3}}}[/tex]
[tex]y-intercept\ \text{for}\ x=0:\\\\-3(0)+9y=14\\0+9y=14\\9y=14\qquad\text{divide both sides by 9}\\\boxed{y=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
