Answer:
Equation of line in [tex]x+y=10[/tex]
Step-by-step explanation:
The intercept form of line is given as,
[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex]
Where, line has x intercept as a and y intercept as b.
Given that x intercept as [tex]\left(c,0\right)[/tex], so [tex]a = c[/tex]. Also y intercepts as [tex]\left(0,c\right)[/tex], so [tex]b = c[/tex].
Substituting the value in intercept form of line,
[tex]\dfrac{x}{c}+\dfrac{y}{c}=1[/tex]
Since denominator are same,
[tex]\dfrac{x+y}{c}=1[/tex]
Multiplying by c on both sides,
[tex]x+y=c[/tex]
Given that point [tex]\left(4,6\right)[/tex] lies on the line. So [tex]x = 4[/tex] and [tex]y = 6[/tex].
Substituting the value,
[tex]4+6=c[/tex]
[tex]10=c[/tex]
Substituting the value in [tex]x+y=c[/tex]
[tex]x+y=10[/tex]
Therefore, equation of line in the standard form of equation of line is [tex]x+y=10[/tex].
