practice solving problems with two - variable linear inequalities. which shows the graph of the solution set…

Answer:

First, rewrite the inequality $6x + 4y<12$ in slope - intercept form $y=mx + b$.

Step1: Isolate $y$

Subtract $6x$ from both sides: $4y<-6x + 12$.

Step2: Solve for $y$

Divide each term by $4$: $y<-\frac{3}{2}x+3$. The boundary line is $y =-\frac{3}{2}x + 3$, which has a $y$-intercept of $3$ and a slope of $-\frac{3}{2}$. Since the inequality is $y<-\frac{3}{2}x + 3$, the boundary line is dashed (because the inequality is strict, $<$ not $\leq$) and the shading is below the line.

To determine the correct graph among the options, look for the graph with a dashed line having a $y$-intercept at $3$ and a slope of $-\frac{3}{2}$ (going down 3 units for every 2 units to the right) and the region below the line shaded. Without seeing the specific labels on the options, the general way to identify the correct graph is based on these characteristics of the line and the shading.