About Linear Functions:
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A linear function graph looks like a straight line. There can be a negative slope or positive slope of a linear graph. The graph can also go straight horizontally or vertically. The domain of a linear is called the input or independent variable. The range of a linear is called the output or dependent variable. There are three different forms of linear. The three form are; slope intercept form, standard form, and point-slope form. Linear functions are used every day in the real world. It is used to estimate the cost of most services like taxi company or wages earned.
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Numerical example:
![Picture](/uploads/9/0/5/9/90595291/screen-shot-2016-11-26-at-9-52-52-am.png?250)
y=2x+0
Verbal Example:
The number of children in the after school program increase by two each school year. Year 1 enrollment= 2 students Year 2 enrollment=4 students Year 3 enrollment=6 students Year 4 enrollment = 8 students
Linear function equation: E = 2+2y
Let E= Enrollment
Let Y= # of years
2= start value
2Y= rate of change
Linear function equation: E = 2+2y
Let E= Enrollment
Let Y= # of years
2= start value
2Y= rate of change
Question #1: Find the linear equation of a function who has a slope of 5 and a coordinate of (10, 20)
My Solution: y-10=5(x+20)
y-10=5x+100
y=5x+110
Using the point slope form i plug in 5 for the slope, 10 subtracting from y and 20 adding to x in the parentheses.
Then I distribute 5 to the x and positive 20.
The equation simplify to "y-10=5x+100".
To get the y by itself i add 10 to both sides.
The Linear equation simplify to y=5x+110.
My Solution: y-10=5(x+20)
y-10=5x+100
y=5x+110
Using the point slope form i plug in 5 for the slope, 10 subtracting from y and 20 adding to x in the parentheses.
Then I distribute 5 to the x and positive 20.
The equation simplify to "y-10=5x+100".
To get the y by itself i add 10 to both sides.
The Linear equation simplify to y=5x+110.
![Picture](/uploads/9/0/5/9/90595291/screen-shot-2016-11-01-at-1-47-45-pm_1.png?250)
Question #2: Determine the linear function of the table.
My Solution: y-2=(4/1)(x+4)
y-2=4(x+4)
y-2= 4x+16
y=4x+18
To determine the linear function I first found the slope by subtracting y2-y1 (4-2) over x2-x1 (2-1). To get a slope of (4/1).
Then i use the point slope form by using the points (2,4).I distribute the 4 to (x+4), which simplify to 4x+16. Then i added two to both sides to get my linear function of Y=2x+18
My Solution: y-2=(4/1)(x+4)
y-2=4(x+4)
y-2= 4x+16
y=4x+18
To determine the linear function I first found the slope by subtracting y2-y1 (4-2) over x2-x1 (2-1). To get a slope of (4/1).
Then i use the point slope form by using the points (2,4).I distribute the 4 to (x+4), which simplify to 4x+16. Then i added two to both sides to get my linear function of Y=2x+18
Real Life Application of Linear Function:
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Real Life Application of linear function: |
If a taxi company charges a flat rate of $5.00 and 25 cents per mile traveled. How much money will you spend going to a party that is 15 miles away from your current location?
1. Come up with a linear equation. y=$5.00+.25m; m=miles 2. Plug in 15 for m and solve y=$5.00+.25(15) y=$5.00+.25(15)=$8.75 You will spend $8.75 on a taxi going to a party that is 15 miles away from your current location. |