money the graph shows a proportional relationship between a persons total savings in dollars and the number…

Explanation:

Step1: Identify two points on the line

Let's take two points from the graph: (0, 500) and (10, 0).

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=500,x_2 = 10,y_2 = 0$. So, $m=\frac{0 - 500}{10-0}=\frac{- 500}{10}=-50$.

Step3: Write the equation of the line

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept $b$ is the value of $y$ when $x = 0$. From the point $(0,500)$, we know that $b = 500$. So the equation is $y=-50x + 500$. But since it is a proportional relationship (the line passes through the origin in a true proportionality sense if we consider the general form $y=kx$ after some transformation of the context), and we can rewrite it in terms of the relationship between savings $y$ and number of weeks $x$ as $y = 500-50x$. If we assume the initial savings is $500$ and it decreases by $50$ per week.

Answer:

$y=-50x + 500$