Question

1. what is the equation of the line below?

Explanation:

Step1: Identify two points on the line

Looking at the graph, let's take three visible red points. Let's pick \((2, 5)\), \((4, 4)\), and \((6, 3)\) (assuming the grid has each square as 1 unit). Let's use \((2, 5)\) and \((4, 4)\) for calculation.

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,5)\) and \((x_2,y_2)=(4,4)\). Then \(m=\frac{4 - 5}{4 - 2}=\frac{-1}{2}=-\frac{1}{2}\).

Step3: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((2,5)\) and \(m =-\frac{1}{2}\), we have \(y - 5=-\frac{1}{2}(x - 2)\).
Expand the right - hand side: \(y - 5=-\frac{1}{2}x + 1\).
Add 5 to both sides: \(y=-\frac{1}{2}x+1 + 5\), so \(y=-\frac{1}{2}x + 6\). We can verify with another point, say \((4,4)\). Substitute \(x = 4\) into \(y=-\frac{1}{2}x + 6\), we get \(y=-\frac{1}{2}(4)+6=-2 + 6 = 4\), which matches the point \((4,4)\). And for \((6,3)\), \(y=-\frac{1}{2}(6)+6=-3 + 6 = 3\), which also matches.

Answer:

\(y =-\frac{1}{2}x + 6\)