Find the equation of the linear function represented by the table below in slope-
1 answer:
The picture attached has the table that repfesents the linear function to find the equation.
Answer:
- y = 10x - 6
Explanation:
A<em> linear function</em> is characterized by a constant slope and a unique y-intercept.
Let m be the slope and b the y-intercept of a linear function. Then, s<em>lope-intercept</em> equation has the form:
- y = mx + b.
Using any two pair of points (x,y) from the table you can determine the values of m and b.
The table is:
x 0 1 2 3 4
y -6 4 14 24 34
You know that it is a linear function because for constant increases of the x-values (1 unit in the table) there is a constant increase of the y-values (10 in the table).
The slope, m, is calculated as:
- m = [change in y] / [change in x] = Δy / Δx = [14 - 4] [2 - 1] = 10
As said, you could have used any two points to calculate m,
The y-intercept, b, is the value of the function, y, when x = 0.
- From the table you can observe that when x = 0, the value of y is - 6; so b = - 6.
Thus, the equation of the linear function represented in the table in slope-intercept form is:
- y = 10x - 6.
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Answer:
a) 63.6 ft
b) 1.99 seconds
c) 4.98 seconds
Step-by-step explanation:
a) The object will reach maximum height when its final velocity, v, is 0 m/s.
We apply one of Newton's equations of motion to solve this:
where u = initial velocity = 64 ft/s
g = acceleration due to gravity = 32.2 ft/s
h = height reached by object.
Note: the equation has a negative sign because the object is going upwards, against gravity.
Hence:
The object is now 63.6 ft above the platform (143.6 ft above the ground).
b) Time taken to get to that height can be gotten by using another one of Newton's equations:
=>
It took the object 1.99 secs to get to that height.
c) When the object begins falling to ground level, it is at a height, h = 143.6 ft and begins moving at initial velocity, u = 0 m/s.
Applying another of Newton's equations of motion, we have that:
where t is the time taken to hit the floor after it begins its descent.
Therefore,
This is the time it will take the object to hit the floor after it begins its descent.
Therefore, the total time it will take for the object to hit the ground after it is launched will be:
T = time taken to reach maximum height + time taken to hit the floor after it begins descending
T = 1.99 + 2.99
T = 4.98 seconds