Question

write an equation of the line below.
your answer

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, 4)\) (the y - intercept) and \((- 6, 6)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(-6,6)\). Then \(m=\frac{6 - 4}{-6-0}=\frac{2}{-6}=-\frac{1}{3}\)? Wait, no, wait another point. Wait, maybe I picked the wrong points. Wait, the line passes through \((0,4)\) and let's take another point. Wait, the point at \(x = - 5\)? No, wait the blue dot is at \((-6,6)\) and \((0,4)\)? Wait, no, when \(x=-6\), \(y = 6\); when \(x = 0\), \(y=4\). Wait, but also, let's check the slope between \((0,4)\) and \((5,2)\) (since when \(x = 5\), \(y=2\) maybe? Wait, no, the slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0,4)\) and \((5,2)\). Then \(m=\frac{2 - 4}{5-0}=\frac{-2}{5}\). Ah, that's better. So \(m =-\frac{2}{5}\).

Step3: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept. From the graph, the line crosses the y - axis at \((0,4)\), so \(b = 4\). And we found that \(m=-\frac{2}{5}\). So the equation of the line is \(y=-\frac{2}{5}x + 4\).

Answer:

\(y =-\frac{2}{5}x + 4\)