Question

card 5
a graph:
card 6
a equation:
b dollars

Explanation:

Step1: Identify the type of graph

The graph is a straight line passing through the origin, so it represents a proportional relationship, i.e., a linear equation of the form \( y = mx \), where \( m \) is the slope.

Step2: Calculate the slope

To find the slope \( m \), we can use two points on the line. Let's take the origin \((0,0)\) and another point, say \((2,2)\) (since when \( x = 2 \), \( y = 2 \) from the graph). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Plugging in \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,2)\), we get \( m=\frac{2 - 0}{2 - 0}=\frac{2}{2} = 1 \).

Step3: Write the equation

Since the slope \( m = 1 \) and the y - intercept \( b = 0 \) (it passes through the origin), the equation of the line is \( y=x \).

Answer:

The equation of the line in the graph is \( y = x \)