Answer:
y = -x + 6
Step-by-step explanation:
[tex]\text{The intercept form of an equation of a line:}\\\\\dfrac{x}{a}+\dfrac{y}{b}=1\\\\a-x\ intercept\\b-y\ intercept\\\\\text{We have:}\\\\point\ (2,\ 4)\to x=2,\ y=4\\a=c\\b=c\\\\\text{Substitute:}\\\\\dfrac{2}{c}+\dfrac{4}{c}=1\\\\\dfrac{2+4}{c}=1\\\\\dfrac{6}{c}=1\qquad\text{multiply both sides by}\ c\neq0\\\\6=c\to c=6[/tex]
[tex]\text{Put it to the equation in the intercept form:}\\\\\dfrac{x}{6}+\dfrac{y}{6}=1\\\\\dfrac{x+y}{6}=1\qquad\text{multiply both sides by 6}\\\\x+y=6\qquad\text{subtract}\ x\ \text{from both sides}\\\\y=-x+6[/tex]
