GRAPHING LINEAR FUNCTIONS
About "Graphing linear functions"
Graphing linear functions :
The table shows the total amount of rain that falls in various amounts of time during aheavy rain.
If "x" denotes time and "y" denotes total amount of rain, then the relationship between time and total amount of rain can be represented by the equation y = 1.5x, The graph of the relationship will be a line, so the equation is a linear equation. Since there is exactly one value of y for each value of x, the relationship is a linear function.
Graphing linear functions - Examples
Example 1 :
The temperature at dawn was 8 °F and increased steadily 2 °F every hour. The equation y = 2x + 8 gives the temperature y after x hours. State whether the relationship between the time and the temperature is proportional or non proportional. Then graph the function.
Solution :
Step 1 :
The given equation y = 2x + 8 is in slope-intercept form linear equation. That is, y = mx + b.
When we compare the equation y = 2x + 8 with y = mx + b, we get m = 2 and b = 8.
Therefore, the equation is a linear equation. Since b ≠ 0, the relationship is non proportional.
Step 2 :
Choose several values for the input x. Plug these values for x in the equation to find the output y.
x
0
2
4
6
2x + 8
2(0) + 8
2(2) + 8
2(4) + 8
2(6) + 8
y
8
12
16
20
(x, y)
(0, 8)
(2, 12)
(4, 16)
(6, 20)
Step 3 :
Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.
Example 2 :
The temperature of a fish tank was 82 °F and decreased steadily 2 °F every hour. The equation y = -2x + 82 gives the temperature y after x hours. State whether the relationship between the time and the temperature is proportional or non proportional. Then graph the function.
Solution :
Step 1 :
The given equation y = -2x + 82 is in slope-intercept form linear equation. That is, y = mx + b.
When we compare the equation y = -2x + 82 with y = mx + b, we get m = -2 and b = 82.
Therefore, the equation is a linear equation. Since b ≠ 0, the relationship is non proportional.
Step 2 :
Choose several values for the input x. Plug these values for x in the equation to find the output y.
x
0
1
2
3
4
5
-2x + 82
-2(0) + 82
-2(1) + 82
-2(2) + 82
-2(3) + 82
-2(4) + 82
-2(5) + 82
y
82
80
78
76
74
72
(x, y)
(0, 82)
(1, 80)
(2, 78)
(3, 76)
(4, 74)
(5, 72)
Step 3 :
Graph the ordered pairs. Then draw a line through the points to represent the solutions of the function.
After having gone through the stuff given above, we hope that the students would have understood "Graphing linear functions".
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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
