Question

The equation d=4-1/15t represents your distance from home, d, for each minute you walk, t. If you graphed this equation, determine the meaning of the slope in the situation

Answer 1

Answer: the slope is -1/15 and it means that the distance from home decreases 1/15 units per minute of walk, which indicates the your are going home.

Explanation:

The equation d = 4 - (1/5)t has these features:

• it is a linear (first degree) equation/
• d is the dependent variable, distance from home.
• t is the independent variable, minutes of walk
• 4 is the constant term and it is the value of d when t = 0, which means that it is the vertical axis intercept and represents the initial distance from home.
• - ( 1/15) is the coefficient of the independent variable, it is the slope of the equation, and means the rate of change of the distance per minute of walk.
• this slope, since it is negative, means that the distance decreases as times goes on. It means that each minute of walk the distance decreases 1/15 unit.
• you can find when the distance is zero, by doing the variable d = 0:

         d = 0 = 4 - (1/15)t ⇒ t = 4×15 = 60 min.

The given equation, d = 4 - (1/5)t is a linear equation, whose y-intercept form is y = mx + b.

• m is the slope, therefore it is - 1/15.
• 4 is the y-intercept, therefore it is 4.

The domain of the function is the interval [0, 60], meaning that those are the minutes of the walk.

The range of the function is the interval [4, 0] meaning that the distance goes from 4 to 0 units.

You have plenty information to do the graph:

• label the horizontal axis t in minutes
• do marks at 0, 5, 10, 15, 20, 25, .... up to 60 on the horizontal axis
• lable the vertical axis d
• do marks at 4, 3, 2, 1, on the vertical axis
• draw the points (0, 4) and (60,0)
• draw a segment joining those two points.

You can see the graph in the image attached.