Rewrite the fractions with their LCD.
1 answer:
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Answer:
a) The slope of the function is 3.
c) The equation is represented by .
d) The y-intercept of the function is 35.
Step-by-step explanation:
a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:
(1)
Where:
- Slope, measured in number of pieces per minute.
- Time, measured in minutes.
- Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.
- Current number of pieces of mail that must be hand-sorted, measured in pieces.
From Geometry, we know that a line can be formed by know two distinct points. If we know that and
, then the following system of linear equations is formed:
(2)
(3)
The solution of the system of equations is:
and
The slope of the function is 3.
c) By (1) and using results from a) we conclude that the equation function is:
(4)
d) The y-intercept of the function is 35.
Answer:
B, C
Step-by-step explanation:
The equation of a line can be given by y -y₁= m(x -x₁), where m is the slope. This is also known as the point-slope form.
Slope of the line
= -4
<em>Substitute m= -4 into the equation:</em>
y -y₁= -4(x -x₁)
<em>Substitute a pair of coordinates into (x₁, y₁):</em>
Let's start by substituting (1, 2).
y -2= -4(x -1)
This gives us the same equation as D, making D an incorrect option. Note that the question asks for which is not the correct equation.
Let's change the above into the slope-intercept form, where by y is the subject of formula.
<em>Start by expanding the right-hand side:</em>
y -2= -4x +1
<em>+</em><em>2</em><em> on both sides:</em>
y= -4x +3
This equation is not the same as C. C is thus the correct option.
Let's check for options A and B.
The equation in option B is not the correct equation either as they have substituted (2, 1) instead of (1, 2) into (x₁, y₁). Thus, option B is also correct.
y -y₁= -4(x -x₁)
Substitute (3, -6) into (x₁, y₁):
y -(-6)= -4(x -3)
y +6= -4(x -3)
This is the same as option A, making option A incorrect too.