The equations in slope-intercept form for the rainfall data are:
State A: y = -0.4x + 18
State B: y = -0.2x + 14
Finding Equations in Slope-Intercept Form
We need to find the equations in slope-intercept form for the rainfall data of State A and State B.
Step 1: Calculate the slope
The slope (m) represents the change in rainfall per year. We can calculate it using the formula:
m = (y2 - y1) / (x2 - x1)
For State A:
m = (17.6 - 18) / (2017 - 2016) = -0.4 / 1 = -0.4
For State B:
m = (13.8 - 14) / (2017 - 2016) = -0.2 / 1 = -0.2
Step 2: Find the Y-intercept
The Y-intercept (b) represents the initial rainfall level in 2016.
For State A:
b = 18
For State B:
b = 14
Step 3: Write the equations
The slope-intercept form is:
y = mx + b
For State A:
y = -0.4x + 18
For State B:
y = -0.2x + 14
Therefore, the equations in slope-intercept form for the rainfall data are:
State A: y = -0.4x + 18
State B: y = -0.2x + 14
Complete question:
Neighboring states are concerned about global warming and rainfall. They have kept data on their rainfall for the past three years, shown in the table below.
YEAR 2016 2017 2018
State A 18 17.6 17.2
State B 14 13.8 13.6
Write the equations in slope-intercept form. State A equation: State B equation: