Question

1. directions

first, select the line a button to graph the line and choose a line style. then, select the solution set button and choose the shaded region.
graph the following inequality: ( y < -2x + 5 ).

Explanation:

Step1: Identify boundary line

The inequality $y < -2x + 5$ has a boundary line $y = -2x + 5$. Since the inequality is strict ($<$), use a dashed line.

Step2: Find intercepts for the line

• y-intercept: Set $x=0$, so $y = -2(0) + 5 = 5$. Point: $(0, 5)$
• x-intercept: Set $y=0$, so $0 = -2x + 5 \implies 2x = 5 \implies x = \frac{5}{2} = 2.5$. Point: $(2.5, 0)$

Step3: Test a point for shading

Use the origin $(0,0)$: $0 < -2(0) + 5 \implies 0 < 5$, which is true. Shade the region containing $(0,0)$.

Answer:

1. Graph the dashed line $y=-2x+5$ using intercepts $(0, 5)$ and $(2.5, 0)$.
2. Shade the region below (and to the right of) this dashed line.