Question

In the line $4x+7y+c=0$, the sum of the $x$- and $y$- intercepts is $22$. Find $c$.

Answer 1

-56

Explanation:

x-intercept
`\Rightarrow y=0`

y-intrcept
`\Rightarrow x=0`

Substitute x=0 and y=0 into the line equation:

`4\cdot 0+7y+c=0\Rightarrow 7y+c=0,\ \\7y=-c\\\\y=-(c)/(7)`

and

`4x+7\cdot 0+c=0\Rightarrow 4x+c=0,\ \\4x=-c\\\\x=-(c)/(4)`

The sum of x- and y- intercepts is 22, so

`-(c)/(4)+\left(-(c)/(7)\right)=22`

Multiply it by 28:

`-7c-4c=22\cdot 28\\ \\-11c=22\cdot 28\\ \\c=-2\cdot 28=-56`