Question

1. gridded response use the graph to determine the solution to the equation $-\frac{1}{3}x + 1 = 0$?

Explanation:

Step1: Analyze the equation meaning

The equation \(-\frac{1}{3}x + 1 = 0\) represents finding the \(x\)-intercept of the line \(y = -\frac{1}{3}x + 1\), because when \(y = 0\), the equation becomes \(-\frac{1}{3}x + 1 = 0\).

Step2: Find the x-intercept from graph

Looking at the graph, the line crosses the \(x\)-axis (where \(y = 0\)) at \(x = 3\). We can also solve the equation algebraically to verify:
Start with \(-\frac{1}{3}x + 1 = 0\).
Subtract 1 from both sides: \(-\frac{1}{3}x = - 1\).
Multiply both sides by \(-3\): \(x = (-1)\times(-3)=3\).

Answer:

3