Question

svlc algebra 1a - standard (15260)
graphing two - variable linear inequalities
which linear inequality is represented by the graph?
$y \geq \frac{1}{3}x - 4$
$y \leq \frac{1}{3}x - 4$
$y \geq \frac{1}{3}x + 4$
$y < \frac{1}{3}x + 4$

Explanation:

Step1: Determine the slope and y-intercept of the line

The line passes through the point \((0, -4)\) (so the y-intercept \(b = -4\)) and we can calculate the slope \(m\). Let's take another point, say when \(x = 3\), \(y=-3\) (from the line). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - (-4)}{3 - 0}=\frac{1}{3}\). So the equation of the line is \(y=\frac{1}{3}x - 4\).

Step2: Determine the inequality symbol

The shaded region is above the line, and the line is solid (which means the inequality includes equality, so we use \(\geq\) or \(\leq\)). Since the shaded area is above the line \(y = \frac{1}{3}x-4\), the inequality is \(y\geq\frac{1}{3}x - 4\).

Answer:

\(y \geq \frac{1}{3}x - 4\)