Question

Question was provided via image upload.

Explanation:

Step1: Identify two points on the line

We can see that the line passes through \((0, 1)\) (the y - intercept) and \((1, 0)\) (or we can also use other points like \((-3, 4)\) and \((3, -2)\) for better calculation of slope). Let's take two clear points: when \(x = 0\), \(y=1\) (point \(A(0,1)\)) and when \(x = 1\), \(y = 0\) (point \(B(1,0)\)).

Step2: Calculate the slope \(m\)

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1 = 1,x_2=1,y_2 = 0\) into the formula, we get \(m=\frac{0 - 1}{1-0}=\frac{- 1}{1}=- 1\).

Step3: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-1\) and from the point \((0,1)\), the y - intercept \(b = 1\). So the equation of the line is \(y=-x + 1\).

(If the problem was to find the equation of the line or analyze its slope, this is the process. Since the problem was not clearly stated, but based on the graph, a common task is to find the equation or slope. Assuming we need to find the slope - intercept form equation)

Answer:

The equation of the line is \(y=-x + 1\) (or the slope is \(- 1\) and y - intercept is \(1\))