which linear inequality is represented by the graph?\n$yleq2x + 4$\n$yleq\frac{1}{2}x+3$\n$ygeq\frac{1}{2}x…
which linear inequality is represented by the graph?\n$yleq2x + 4$\n$yleq\frac{1}{2}x+3$\n$ygeq\frac{1}{2}x + 3$\n$ygeq2x + 3$
Answer
Answer:
C. $y\geq\frac{1}{2}x + 3$
Explanation:
Step1: Find the slope
The line passes through $(0,3)$ and $(- 6,0)$. Slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3-0}{0 + 6}=\frac{1}{2}$.
Step2: Find the y - intercept
The line intersects the y - axis at $(0,3)$, so $b = 3$. The equation of the line is $y=\frac{1}{2}x+3$.
Step3: Determine the inequality
The line is solid and the shaded region is above the line, so the inequality is $y\geq\frac{1}{2}x + 3$.