Which graph illustrates the inequality $y + 4 \leq \frac { 1 } { 9 } x$ ?

Question

Quizplus · Accepted Answer

To graph the inequality $y + 4 \leq \frac{1}{9}x$, we first need to rearrange it into slope-intercept form: $y \leq -\frac{1}{9}x - 4$. The inequality symbol ($\leq$) indicates that the solution includes any point on the line $y = -\frac{1}{9}x - 4$ as well as any points below the line.

Looking at graph A, we can see that the line is incorrect - it appears to have a positive slope rather than the expected negative slope. This is probably because of a sign error.

Graph B, on the other hand, shows the correct line with the correct slope and y-intercept. However, it incorrectly includes points above the line, rather than below it. To fix this, we need to shade in the area below the line, which is the solution to the inequality.

Therefore, the correct choice is B.

Which Graph Illustrates the Inequality y+4≤19xy + 4 \leq \frac { 1 } { 9 } xy+4≤91​x

Which Graph Illustrates the Inequality $y + 4 \leq \frac { 1 } { 9 } x$