A graph has month on the x-axis and saved (money) on the y-axis. Points are at (0, 3,000), (2, 2,450), and (5, 1,625).

Question

The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form.

y-intercept =

Answer 1

To find the y-intercept and the slope for the given points, we first identify two key components:

1. Y-Intercept: This is the value of $y$ when $x=0$. According to the point (0, 3,000), the y-intercept is 3,000.

   Therefore, the y-intercept is: $$\text{y-intercept}=3000$$

2. Slope: The slope $m$ is calculated using two points on the graph. The formula for the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2-y_1}{x_2-x_1}$$

   Let's calculate the slope using the points (0, 3000) and (2, 2450):

   • $(x_1,y_1)=(0,3000)$
   • $(x_2,y_2)=(2,2450)$

   Applying the slope formula: $$m=\frac{2450-3000}{2-0}=\frac{-550}{2}=-275$$

Now we can write the equation of the line in slope-intercept form $y=mx+b$:

Using $m=-275$ and the y-intercept $b=3000$:

$$y=-275x+3000$$

So to summarize:

• Y-Intercept: $3000$
• Slope: $-275$

The equation in slope-intercept form is: $$y=-275x+3000$$