Question

State and describe the meaning of the x- & y-intercepts for the below table. Then find anddescribe the meaning of the slope.Value of Sam's TruckTime Value ($years)025.000220,000415,000610,00085,000100220.00015.000610.00085.000100

Answer 1

We would start by arranging the points given as ordered pairs. Let the time in years be x, and let the value in dollars be y. That mans we would have the following orederd pairs;

`\begin{gathered} (0,25000) \\ (2,20000) \\ (4,15000) \\ (6,10000) \\ (8,5000) \\ (10,0) \end{gathered}`

The x-intercept is the point where the line of this equation crosses the x axis (that is the point at where y equals 0). This means the x-intercept is 10, that is when

y = 0, x = 10.

Similarly, the y-intercept is 25,000, that is when

x = 0, y = 25,000

To find the slope, we use the formula shown below;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(20000-25000)/(2-0) \\ m=(-5000)/(2) \\ m=-2500 \end{gathered}`

The slope (which is denoted as m) is derived as -2500.

The value of the slope is negative, that is -2500 and that means there is an inverse relationship between both the time in years and the value in dollars. In other words, as the years increase, the value in dollars decrease. As one value goes up, the other one comes down, and vice versa. That is the meaning of a negative slope.