Math  /  Algebra

QuestionThe number of households in a local school district has been increasing linearly over the last ten years. In 2010, there were 985 households, and in 2020 there were 1579 households.
Question 2/10
Use this information to create a linear model for the number of households in the school district. Let H represent the number of households at tt represent the number of years since 2010.

Studdy Solution

STEP 1

1. The number of households is increasing linearly over time.
2. In 2010, there were 985 households.
3. In 2020, there were 1579 households.
4. H H represents the number of households.
5. t t represents the number of years since 2010.

STEP 2

1. Identify the known points on the line.
2. Calculate the slope of the line.
3. Write the equation of the line in slope-intercept form.
4. Interpret the linear model.

STEP 3

Identify the known points on the line.
The points are given by the years and the corresponding number of households: - In 2010 (t=0 t = 0 ), H=985 H = 985 . - In 2020 (t=10 t = 10 ), H=1579 H = 1579 .

STEP 4

Calculate the slope of the line.
The slope m m is calculated using the formula: m=H2H1t2t1 m = \frac{H_2 - H_1}{t_2 - t_1}
Substitute the known values: m=1579985100 m = \frac{1579 - 985}{10 - 0} m=59410 m = \frac{594}{10} m=59.4 m = 59.4

STEP 5

Write the equation of the line in slope-intercept form.
The slope-intercept form of a line is given by: H=mt+b H = mt + b
We know m=59.4 m = 59.4 and the point (0,985) (0, 985) is on the line, so b=985 b = 985 .
Thus, the equation is: H=59.4t+985 H = 59.4t + 985

STEP 6

Interpret the linear model.
The linear model H=59.4t+985 H = 59.4t + 985 indicates that the number of households increases by 59.4 each year since 2010, starting from 985 households.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord