Answer:
-56
Step-by-step explanation:
x-intercept [tex]\Rightarrow y=0[/tex]
y-intrcept [tex]\Rightarrow x=0[/tex]
Substitute x=0 and y=0 into the line equation:
[tex]4\cdot 0+7y+c=0\Rightarrow 7y+c=0,\ \\7y=-c\\\\y=-\dfrac{c}{7}[/tex]
and
[tex]4x+7\cdot 0+c=0\Rightarrow 4x+c=0,\ \\4x=-c\\\\x=-\dfrac{c}{4}[/tex]
The sum of x- and y- intercepts is 22, so
[tex]-\dfrac{c}{4}+\left(-\dfrac{c}{7}\right)=22[/tex]
Multiply it by 28:
[tex]-7c-4c=22\cdot 28\\ \\-11c=22\cdot 28\\ \\c=-2\cdot 28=-56[/tex]
