Question

1. what is the equation of the line below?

Explanation:

Step1: Identify two points on the line

Looking at the graph, let's assume the grid has each square with side length 1. Let's find two clear points. Let's say the left point is \((-8, 4)\) and the right point is \((8, 0)\) (we can check the coordinates by counting the grid squares: from the origin, moving left 8 units (x = -8) and up 4 units (y = 4) for the first point, and right 8 units (x = 8) and y = 0 for the second point).

Step2: Calculate the slope (m)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-8,4)\) and \((x_2,y_2)=(8,0)\). Then \(m=\frac{0 - 4}{8 - (-8)}=\frac{-4}{16}=-\frac{1}{4}\).

Step3: Find the y-intercept (b)

We can use the slope-intercept form \(y = mx + b\). Let's use one of the points, say \((8,0)\). Substitute \(x = 8\), \(y = 0\), and \(m=-\frac{1}{4}\) into the equation: \(0=-\frac{1}{4}(8)+b\). Simplify: \(0=-2 + b\), so \(b = 2\).

Step4: Write the equation

Using \(y = mx + b\) with \(m=-\frac{1}{4}\) and \(b = 2\), the equation is \(y=-\frac{1}{4}x + 2\). Wait, let's check with the other point \((-8,4)\): \(y=-\frac{1}{4}(-8)+2=2 + 2=4\), which matches. So the equation is correct.

Answer:

\(y = -\frac{1}{4}x + 2\)