Question

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

Explanation:

Step1: Find the slope - intercept form of the boundary line

The boundary line passes through the points \((0,0)\) and \((5,8)\). The slope \(m\) of the line is \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8 - 0}{5 - 0}=\frac{8}{5}\). Using the slope - intercept form \(y = mx + b\) with \((x,y)=(0,0)\) and \(m=\frac{8}{5}\), we get \(y=\frac{8}{5}x\) or \(8x-5y = 0\).

Step2: Determine the inequality

The shaded region is below the line and the line is solid. For a line \(Ax+By = C\), if the region below the line is shaded and the line is solid, the inequality is \(Ax + By\leq C\). Rewriting \(8x-5y = 0\) in the form of the given options, we have \(8x-5y\leq0\) or \(8x - 5y\geq0\). Since the shaded region is below the line \(y=\frac{8}{5}x\), the inequality is \(8x-5y\leq0\) or \(5y-8x\geq0\).

Answer:

A. \(8x - 5y\leq0\)