Question

1. what is the equation of the line shown in the graph?

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 3)\) (the y - intercept) and \((- 6,0)\) (we can also use other points, for example, when \(x = 0\), \(y=3\); let's find another point. Let's take two clear points: \((0, 3)\) and \((-6,0)\) or \((0,3)\) and \((4,5)\) (by counting the grid). Wait, let's use \((0,3)\) and \((4,5)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \( (x_1,y_1)=(0,3)\) and \( (x_2,y_2)=(4,5)\). Then \(m=\frac{5 - 3}{4 - 0}=\frac{2}{4}=\frac{1}{2}\). Alternatively, using \((0,3)\) and \((-6,0)\), \(m=\frac{0 - 3}{-6 - 0}=\frac{- 3}{-6}=\frac{1}{2}\).

Step2: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that the line crosses the y - axis at \((0,3)\), so \(b = 3\). And we found that the slope \(m=\frac{1}{2}\).
So the equation of the line is \(y=\frac{1}{2}x + 3\).

Answer:

\(y=\frac{1}{2}x + 3\)