Answer :
Answer:
See the below works.
Step-by-step explanation:
We can find the x-intercept in this scenario by first finding the function of time.
[tex]\begin{array}{c|c}Time(x)&Distance(f(x))\\\cline{1-2}0&36\\3&32\\6&28\\9&24\\12&20\end{array}[/tex]
From the table, we can find that:
- the distance at the starting point (y-intercept) is 36 meters.
- for every 3 minutes, the distance decreases by 4 meters. Since the decrease rate is constant, then the function is a linear function.
We can find the function of time by using the slope-intercept form:
[tex]\boxed{f(x)=mx+c}[/tex]
where:
- [tex]m=\texttt{gradient}[/tex]
- [tex]c=\texttt{y-intercept}[/tex]
To find the gradient, we use this formula:
[tex]\boxed{m=\frac{\Delta f(x)}{\Delta x} }[/tex]
We can pick any 2 pairs of given data to find the differences of f(x) and x. Let's say we pick x₁ = 0 and x₂ = 3, then the f(x)₁ = 36 and f(x)₂ = 32
[tex]\begin{aligned}m&=\frac{\Delta f(x)}{\Delta x} \\\\&=\frac{f(x)_2-f(x)_1}{x_2-x_1} \\\\&=\frac{32-36}{3-0} \\\\&=-\frac{4}{3} \end{aligned}[/tex]
Hence, the function of time:
[tex]f(x)=mx+c[/tex]
[tex]\displaystyle \bf f(x)=-\frac{4}{3} x+36[/tex]
To find the x-intercept, we substitute f(x) with 0:
[tex]\begin{aligned}0&=-\frac{4}{3} x+36\\\\\frac{4}{3} x&=36\\\\x&=36\div\frac{4}{3} \\\\x&=\bf27\end{aligned}[/tex]
X-intercept in this scenario means time needed to arrive school (where the distance f(x) is 0). As x = 27, which means it will take 27 minutes to arrive school.
