Expand and simplify 5(2a – c) + 4(3a + 2c)
2 answers:
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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.
