From the information provided, the inequality representing the combination of codebooks and flashlights is
[tex]c+f\ge50[/tex]
The variable f represents the y variable while the variable c reprsents the x variable. In other words, what we have here could also be written as;
[tex]x+y\ge50[/tex]
In slope-intercept form, this is written as;
[tex]y\ge-x+50[/tex]
Therefore, the inequality here would be expressed in slope-intercept form as;
[tex]f\ge-c+50[/tex]
The other inequality is written out as
[tex]2c+5f\le175[/tex]
In slope-intercept form, this becomes;
[tex]\begin{gathered} 5f\le-2c+175 \\ \text{Divide both sides by 5} \\ \frac{5f}{5}\le-\frac{2c+175}{5} \\ f\le-\frac{2c}{5}+\frac{175}{5} \\ f\le-\frac{2c}{5}+35 \\ f\le-\frac{2}{5}c+35 \end{gathered}[/tex]
We can now graph both inequalities as follows;
[tex]\begin{gathered} \text{Note that the green region represents the inequality,} \\ f\ge-c+50 \end{gathered}[/tex][tex]\begin{gathered} \text{Also the purple region represents the inequality,} \\ f\le-\frac{2}{5}c+35 \end{gathered}[/tex]
The possible solutions for both inequalities is represented by the region where both colors intersect.
