Answer:
- (3, 21), (6, 12)
- -3
- y -21 = -3(x -3) ⇒ y = -3x +30
- 30 minutes; 3 minutes
Step-by-step explanation:
a) The two marked points have coordinates (days, minutes) = (3, 21) and (6, 12).
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b) The slope is the vertical change (rise) divided by the horizontal change (run). For these two points, that is ...
rise/run = (12-21)/(6-3) = -9/3 = -3 = slope
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c) The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . for slope m through point (h, k)
Using the first point and the slope we found, this is ...
y -21 = -3(x -3) . . . . . point-slope form
Add 21 and eliminate parentheses:
y = -3x +9 +21
y = -3x +30 . . . . . . . . collect terms; slope-intercept form
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d) The initial time is the time corresponding to day 0, the value of y when x=0. It is 30 minutes.
The slope in part (b) tells us the time decreases by 3 minutes per day.
