which is the graph of 4x + 2y < 3?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, solve $4x + 2y<3$ for $y$. Subtract $4x$ from both sides: $2y<-4x + 3$. Then divide by 2: $y<-2x+\frac{3}{2}$.

Step2: Analyze the boundary line

The boundary line of the inequality $y = - 2x+\frac{3}{2}$ has a slope $m=-2$ and a $y$-intercept $b = \frac{3}{2}=1.5$. Since the inequality is $y<-2x+\frac{3}{2}$, the boundary line is dashed (because the inequality is strict, $<$ not $\leq$).

Step3: Test a point

Let's test the point $(0,0)$. Substitute $x = 0$ and $y = 0$ into the original inequality $4x+2y<3$. We get $4(0)+2(0)=0<3$, which is true. So, the region that contains the origin $(0,0)$ is the solution region.

The graph with a dashed line having a negative slope of - 2, $y$-intercept of 1.5 and the region below the line and containing the origin is the correct graph.

Answer:

The graph with a dashed line having slope - 2, $y$-intercept 1.5 and the region below the line that contains the origin.