Question

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is ​​ Point on line: (4, 6) x-intercept: (c, 0) y-intercept: (0, c), c ≠ 0

Answer 1

Answer:

Equation of line in $x+y=10$

Step-by-step explanation:

The intercept form of line is given as,

$\dfrac{x}{a}+\dfrac{y}{b}=1$

Where, line has x intercept as a and y intercept as b.

Given that x intercept as $\left(c,0\right)$, so $a = c$. Also y intercepts as $\left(0,c\right)$, so $b = c$.

Substituting the value in intercept form of line,

$\dfrac{x}{c}+\dfrac{y}{c}=1$

Since denominator are same,

$\dfrac{x+y}{c}=1$

Multiplying by c on both sides,

$x+y=c$

Given that point $\left(4,6\right)$ lies on the line. So $x = 4$ and $y = 6$.

Substituting the value,

$4+6=c$

$10=c$

Substituting the value in $x+y=c$

$x+y=10$

Therefore, equation of line in the standard form of equation of line is $x+y=10$.