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Question:Describe if the relationship is linear. If it is find a rule and write it in symbols. Then check your rule with each input/output pair.
1) z = 1 1 3 5 7 9
w = 12 6 0 6 12 18
Answers:If it's linear, then the graph must be a straight line. The equation for a straight line is: y = mx + b where: m = the slope b = the yintercept The equation for the slope = (y''  y')/(x''  x') Using the values of w as "y", select the first two values for the slope equation: (6  12) = (6 + 12) = 6 Using the values of z as "x", select the first two values for the slope equation: (1   1) = (1 + 1) = 2 Substituting these values into the slope equation: 6/2 = 3 Substitute one set of values into the slope equation to find the yintercept (b value): y = mx + b y = 3x + b (we just solved for the slope) 18 = (3)(9) + b 18 = 12 + b b = 9 Now rewrite the slope equation using the values for slope and yintercept: y = 3x  9 w = 3z  9 (using the variables given in the problem) *** This is one of your answers *** Check your answer by substituting the various values for Z & W @ (1, 12) = 12 = 3  9 (this checks out) @ (1, 6) = 6 = 3  9 (this checks out) @ (3, 0) = 0 = 9  9 (this checks out) @ (5, 6) = 6 = 15  9 (this checks out) @ (7,12) = 12 = 21  9 (this checks out) @ (9, 18) = 18 = 27  9 (this checks out) When we worked the equation, we assumed that Z = xaxis and W = yaxis It is also possible that Z = yaxis and W = xaxis Solve for the slope but this time use Z values in the numerator and W values in the denominator: m = (1   1)/(6   12) = (1 + 1)/ (6 + 12) = 2/6 = 1/3 Using the value for the slope, find the yintercept using the equation: y = mx + b y = (1/3)x + b Substitute a value for "x" and "y": 1 = (1/3)(12) + b 1 = 4 + b b = 3 Your equation becomes: y = (1/3)x + 3 z = (1/3)w + 3 (using the variables given in the problem) *** This is your other answer *** Substitute values to check the math: @ (12, 1) = 1 = 4 + 3 (this checks out) @ (6, 1) = 1 = 2 + 3 (this checks out) @ (0, 3) = 3 = 0 + 3 (this checks out) @ (6, 5) = 5 = 2 + 3 (this checks out) @ (12, 7) = 7 = 4 + 3 (this checks out) @ (18, 9) = 9 = 6 + 3 (this checks out) Cool huh?
Answers:If it's linear, then the graph must be a straight line. The equation for a straight line is: y = mx + b where: m = the slope b = the yintercept The equation for the slope = (y''  y')/(x''  x') Using the values of w as "y", select the first two values for the slope equation: (6  12) = (6 + 12) = 6 Using the values of z as "x", select the first two values for the slope equation: (1   1) = (1 + 1) = 2 Substituting these values into the slope equation: 6/2 = 3 Substitute one set of values into the slope equation to find the yintercept (b value): y = mx + b y = 3x + b (we just solved for the slope) 18 = (3)(9) + b 18 = 12 + b b = 9 Now rewrite the slope equation using the values for slope and yintercept: y = 3x  9 w = 3z  9 (using the variables given in the problem) *** This is one of your answers *** Check your answer by substituting the various values for Z & W @ (1, 12) = 12 = 3  9 (this checks out) @ (1, 6) = 6 = 3  9 (this checks out) @ (3, 0) = 0 = 9  9 (this checks out) @ (5, 6) = 6 = 15  9 (this checks out) @ (7,12) = 12 = 21  9 (this checks out) @ (9, 18) = 18 = 27  9 (this checks out) When we worked the equation, we assumed that Z = xaxis and W = yaxis It is also possible that Z = yaxis and W = xaxis Solve for the slope but this time use Z values in the numerator and W values in the denominator: m = (1   1)/(6   12) = (1 + 1)/ (6 + 12) = 2/6 = 1/3 Using the value for the slope, find the yintercept using the equation: y = mx + b y = (1/3)x + b Substitute a value for "x" and "y": 1 = (1/3)(12) + b 1 = 4 + b b = 3 Your equation becomes: y = (1/3)x + 3 z = (1/3)w + 3 (using the variables given in the problem) *** This is your other answer *** Substitute values to check the math: @ (12, 1) = 1 = 4 + 3 (this checks out) @ (6, 1) = 1 = 2 + 3 (this checks out) @ (0, 3) = 3 = 0 + 3 (this checks out) @ (6, 5) = 5 = 2 + 3 (this checks out) @ (12, 7) = 7 = 4 + 3 (this checks out) @ (18, 9) = 9 = 6 + 3 (this checks out) Cool huh?
Question:identify the domain and range of the function, recall the domain represents the xvalues(independent variables) and the range represents the yvalues(dependent variable). input 2 3 4 5 6
output 3 8 13 18 23
Answers:These are simply the natural numbers, N (or the positive integers, if you prefer) in both domain and range, so it just goes N N.
Answers:These are simply the natural numbers, N (or the positive integers, if you prefer) in both domain and range, so it just goes N N.
Question:whats the relationship between the input and output numbers using an expression. input = t output = n
input(t) 1  2  3  4 
output(n) 2  4  8  16  what does ^ mean?
Answers:2 ^ (t) = n I think that's how you express it, =D
Answers:2 ^ (t) = n I think that's how you express it, =D
Question:Im helping my brother study for his Algebra exam and I came across something that I cant seem to figure out!
heres the question.
Make an imputoutput table for the function using the domain 2,1,0,1, and 2. Thens tate the range of the function.
heres one of the problems they gave y=x+3
I dont know which one is y and which one is x...im just completely lost on this! PLease help!
Answers:i think the domain is the x, soo plug in 2 and all those 4 other numbers into the equation and you get the answer for the y so.. 1,2,3,4,5
Answers:i think the domain is the x, soo plug in 2 and all those 4 other numbers into the equation and you get the answer for the y so.. 1,2,3,4,5
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Application of Leontief InputOutput Model/Production Equation :Solving the Leontief production equation for an economy of 3 sectors (x1, x2, x3) using the Leontief InputOutput Model also know as the Production Equation. An application of Linear Systems. Please Subscribe. More Math Videos to come!