Question

select a linear equation, vertical, and/or x or y to show the inverse vary function? (some text on the left and right is partially unclear, but the main part involves a graph with points like (2,2)? wait, no, looking at the graph, maybe points like (-2, 2)? wait, the grid and the line through the origin, with some points marked. the text on the right: select a linear equation, vertical, and/or x or y to show the inverse vary function? and on the left: graph (the rest unclear).

Explanation:

Step1: Identify two points

From the graph, we can see the line passes through \((0,0)\) and \((-2, 2)\) (or other points like \((-4,4)\), \((-6,6)\) etc.). Let's take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(-2,2)\).

Step2: Calculate the slope

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Substituting the values, we get \(m=\frac{2 - 0}{-2 - 0}=\frac{2}{-2}=- 1\).

Step3: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Since the line passes through \((0,0)\), when \(x = 0\), \(y=0\). Substituting \(x = 0\), \(y = 0\) and \(m=-1\) into \(y=mx + b\), we get \(0=-1\times0 + b\), so \(b = 0\).

So the equation of the line is \(y=-x\) or \(y=-1x+0\).

Answer:

The equation of the line is \(y=-x\) (or \(y = - 1x+0\))