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: \[ y = -275x + 3000 \]