Question

find the equation of each line to reveal the three letter code. answers must be \all caps\ with no spaces.

Explanation:

To solve for the equation of each line, we use the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

For the first (red) line:

Step 1: Find the slope (\(m\))

We can use two points on the line. Let's assume two points \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, we can see that when \(x = 0\), \(y=3\) (y - intercept \(b = 3\)), and when \(x = 1\), \(y = 5\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 3}{1-0}=2\).

Step 2: Write the equation

Using \(y=mx + b\) with \(m = 2\) and \(b = 3\), the equation is \(y=2x + 3\), which corresponds to option \(G\).

For the second (blue) line:

Step 1: Find the slope (\(m\))

We can take two points. Let's say when \(x = 0\), \(y = 0\) (y - intercept \(b = 0\)), and when \(x = 1\), \(y=- 2\). The slope \(m=\frac{-2-0}{1 - 0}=-2\).

Step 2: Write the equation

Using \(y=mx + b\) with \(m=-2\) and \(b = 0\), the equation is \(y=-2x\), which corresponds to option \(H\).

For the third (black) line:

Step 1: Find the slope (\(m\))

We can take two points. Let's say when \(x = 0\), \(y = 2\) (y - intercept \(b = 2\)), and when \(x = 1\), \(y=-1\). The slope \(m=\frac{-1 - 2}{1-0}=-3\).

Step 2: Write the equation

Using \(y=mx + b\) with \(m=-3\) and \(b = 2\), the equation is \(y=-3x + 2\), which corresponds to option \(L\).

The three - letter code is formed by the first letters of the equations of the three lines. The equations correspond to \(G\), \(H\) and \(L\), so the code is \(GHL\).

Answer:

\(GHL\)