Step 1: Read and understand the problem statement.
You are given (time, depth) pairs of (20 s, 8 cm) and (40 s, 0 cm) and asked to write an equation that describes the relationship of depth (y) to time (x).
The rate of change is (0 cm -8 cm)/(40 s -20 s) = -8 cm/(20 s) = -2/5 cm/s. Then in point-slope form using the second point, the linear function rule is
y = (-2/5)(x -40) +0
You can expand this to
y = (-2/5)x +16
y = -0.4x +16 . . . . . . using a decimal number for the slope
_____
If the bathtubs in your "draining race" start with the same level, the one with the steepest slope (-0.5 cm/s) will win.
Answer: y=-6x-57
Step-by-step explanation: the normal format of a linear equation is
y=(slope)x+y intercept. The slope is -6 so y=-6x+y intercept. Plugging in the cordinates, -3=-9(-6)+y intercept. We'll call the y intercept b. -3=54+b. Subtract 54 from both sides of the equation and you get b=-54. The linear equation is
y=-6x-57.
You can check by plugging in x= -9, and y= -3. -3=54-57. -3=-3
Answer is choice C) 4x^2-3x+9
You list off the terms in a way where the largest exponent term comes first, then the second largest exponent is next, and so forth. Note how the last term 9 is the same as 9x^0. The term 3x is equivalent to 3x^1. So what we really have is 4x^2-3x^1+9x^0. The exponents count down: 2, 1, 0