Estimate how many tennis balls can fit into a small room
1 answer:
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The piece-wise linear functions can be written as follows:
.
.
.
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:
.
For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:
.
For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:
m = (-3 - (-5))(3 - 2) = 2.
The rule is:
y = 2x + b.
When x = 2, y = -5, hence:
-5 = 2(2) + b
b = -9.
Hence:
.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
The Slope Intercept form of the equation through the point (0, -4) and
(1, 0) is y = 4 x - 1
Step-by-step explanation:
Here, the given points are A (0,-4) and B(1,0)
Now, slope of the equation with points (a,b) and (c,d) is given as
So, here the slope of the line AB is given as:
⇒ m = 4
Now, by POINT SLOPE form:
The equation with slope m and point (x0 , y0) is represented as :
(y-y0) = m (x-x0)
⇒ The equation of AB is of the form with point (1,0) is
y - 0 = 4 (x -1)
or, y = 4 x - 1
Also, the SLOPE INTERCEPT form of an equation is of the form
y = m x + C ; m = slope and C = y -intercept
Hence, the slope intercept form of the equation through the point (0, -4) and (1, 0) is y = 4 x - 1