Question

during a biology lab, jordan is tracking the growth of bacteria based on change in temperature. the relationship between temperature change, x, and bacteria count, y, is graphed below. which inequality best represents this graph? ① 8x - 5y ≤ 0 ② 8x - 5y > 0 ③ 8x - 5y ≥ 0 ④ 8x - 5y < 0

Explanation:

Step1: Find the equation of the boundary - line

The boundary - line passes through the origin \((0,0)\). Let's assume the equation of the line is \(y = mx + b\). Since \(b = 0\) (passes through the origin), we need to find the slope \(m\). If we take another point on the line, say \((5,10)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 0}{5 - 0}=2\). So the equation of the boundary - line is \(y = 2x\) or \(2x-y=0\).

Step2: Determine the type of the boundary - line and the shaded region

The boundary - line is solid, so the inequality is either \(\geq\) or \(\leq\). The shaded region is above the line \(y = 2x\), which means \(y\geq2x\) or \(2x - y\leq0\).

Answer:

\(2x - y\leq0\)