Q3. - Algebra 1

Question

The table shows the function relating the distance to an amusement park in miles and the time in hours the Torres family has driven. Find the $x$- and $y$- intercepts. Describe what the intercepts mean in this situation.

Step-by-Step Solution

Answer

The $x$- and $y$-intercepts are 4 and 248. 

The $x$-intercept means in this situation that when the distance to an amusement park is 0 miles, the time in hours the Torres family has driven is 4 hours.

The $y$-intercept means in this situation that when the Torres family has driven for 0 hours, the distance to an amusement park is 248 miles.

Step 1. Determine the x -intercept of the given graph.

Let $x$ denotes the time and $y$ denotes the distance.

The $x$-intercept of the graph is the value of the $x$ where the graph cuts the $x$-axis.

That implies the $x$-intercept is the value of $x$ where $y$ is zero.

From the table, it can be noticed that when $y=0$, $x=4$.

Therefore, the $x$-intercept is 4.

Step 2. Determine the y -intercept of the given graph.

The $y$-intercept of the graph is the value of the $y$ where the graph cuts the $y$-axis.

That implies the  $y$-intercept is the value of $y$ where $x$ is zero.

From the table, it can be noticed that when $x=0$, $y=248$.

Therefore, the $y$-intercept is 248.

Step 3. Describe what the intercepts mean in this situation.

The $x$-intercept means in this situation that when the distance to an amusement park is 0 mile, the time in hours the Torres family has driven is 4 hours.

The $y$-intercept means in this situation that when the Torres family has driven for 0 hour, the distance to an amusement park is 248 miles.