6. in 2016, honda sold 4.7 thousand vehicles and in 2019 it sold 5.3 thousand vehicles. (10 pts.) a) use the…

6. in 2016, honda sold 4.7 thousand vehicles and in 2019 it sold 5.3 thousand vehicles. (10 pts.) a) use the data to find a linear function, f(x), that gives the number of honda’s sold in year x.

6. in 2016, honda sold 4.7 thousand vehicles and in 2019 it sold 5.3 thousand vehicles. (10 pts.) a) use the data to find a linear function, f(x), that gives the number of honda’s sold in year x.

Answer

Explanation:

Step1: Define points

Let $x = 0$ represent the year 2016. Then for 2016, the point is $(0,4.7)$ and for 2019 ($x = 3$), the point is $(3,5.3)$.

Step2: Find the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 4.7,x_2=3,y_2 = 5.3$. So $m=\frac{5.3 - 4.7}{3-0}=\frac{0.6}{3}=0.2$.

Step3: Find the y - intercept $b$

The equation of a line is $y=mx + b$. Using the point $(0,4.7)$ and $m = 0.2$, when $x = 0,y=b$. So $b = 4.7$.

Step4: Write the linear function

The linear function $f(x)$ has the form $y=mx + b$. Substituting $m = 0.2$ and $b = 4.7$, we get $f(x)=0.2x + 4.7$.

Answer:

$f(x)=0.2x + 4.7$