Answer:
2. f(-2) = 15
3. E = 10h
4. y = 3.50x + 10
5. $41.50
6. y = 3x - 8
7. y = x + 4
Explanation:
#2
Given f(x) = -x² - 4x + 3
f(-2) = (-2)² -4(-2) + 3
= 4 + 8 + 3
= 15
3.At $10 per hour for h hours the earnings will be E = 10h
4. $10 is a constant charge irrespective of number of hours worked
So we get
y = 3.50x + 10
5. For 9 hours, we have x = 9 in the above equation
So y = 3.50(9) + 10
y = 31.50 + 10 = 41.50
So total charge = $41.50
6. The equation of a line in slope-intercept form is
y = mx + b
m is the slope = rate of change of y wrt to x
= (y2 - y1)/(x2 - x1) for any two sets of values (x1, y1) and (x2, y2)
y2 - y1 is known as the rise and x2 - x1 the run
So slope m = rise/run
Take x1 = 0, y1 = -8
x2 = 1, y2 = -5
rise = y2 - y1 = -5 - (-8) = -5 + 8 = 3
run = x2 - x1 = 1 - 0 = 1
Slope m = rise/run = 3/1 = 3
b in the equation is the y-intercept, the value of y when the line crosses the y-axis. this is the value corresponding to x = 0
We see from the table that at x = 0, y = -8
So b = -8
The equation of the line is
y = 3x - 8
(we can verify this by testing some of the values of x with the actual table values and see they are consistent with the equation values but I leave that as an exercise for you)
7. From the graph we can spot 2 clearly defined points which can yield the slope
(x1, y1) = (0, 4) and (x2, y2) = (-4, 0)
Rise = y2 - y1 = 0 - 4 = -4
Run =- 4 - 0 =- 4
Slope m = rise/run = -4/-4 = 1
b = y-intercept = value of y when x = 0 and this is 4
So equation of line is
y = 1x + 4
or
y = x + 4