Question

1. write an equation in slope-intercept form that represents the relationship between x and y as shown in the table.

x	y
10	109,760
20	109,520
30	109,280

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation 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 table, when \(x = 0\), \(y=110000\), so \(b = 110000\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table, for example, \((x_1,y_1)=(0, 110000)\) and \((x_2,y_2)=(10,109760)\).
\(m=\frac{109760 - 110000}{10 - 0}=\frac{- 240}{10}=- 24\)
We can check with another pair of points, say \((x_1 = 10,y_1 = 109760)\) and \((x_2=20,y_2 = 109520)\).
\(m=\frac{109520 - 109760}{20 - 10}=\frac{-240}{10}=-24\). The slope is consistent.

Step3: Write the equation

Now that we have \(m=-24\) and \(b = 110000\), substitute these values into the slope - intercept form \(y=mx + b\).
We get \(y=-24x + 110000\)

Answer:

\(y=-24x + 110000\)