Question

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

Answer 1

Answer:

-56

Step-by-step explanation:

x-intercept $\Rightarrow y=0$

y-intrcept $\Rightarrow x=0$

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

$4\cdot 0+7y+c=0\Rightarrow 7y+c=0,\ \\7y=-c\\\\y=-\dfrac{c}{7}$

and

$4x+7\cdot 0+c=0\Rightarrow 4x+c=0,\ \\4x=-c\\\\x=-\dfrac{c}{4}$

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

$-\dfrac{c}{4}+\left(-\dfrac{c}{7}\right)=22$

Multiply it by 28:

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