Question

write the equation of the line shown.

m: slope
b: y - intercept

$y = mx + b$

$y = $

Explanation:

Step1: Find the y - intercept (b)

The y - intercept is the value of y when x = 0. From the graph, when x = 0, y = 3. So, \(b = 3\).

Step2: Calculate the slope (m)

We can use two points on the line. Let's take the points \((0, 3)\) and \((1, 1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1 = 3,x_2 = 1,y_2 = 1\), we get \(m=\frac{1 - 3}{1 - 0}=\frac{-2}{1}=-2\).

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-2\) and \(b = 3\), we get \(y=-2x + 3\).

Answer:

\(y=-2x + 3\)