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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 y-intercept 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 y-intercept (b value): y = mx + b y = 3x + b (we just solved for the slope) 18 = (3)(9) + b 18 = 12 + b b = -9 Now re-write the slope equation using the values for slope and y-intercept: 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 = x-axis and W = y-axis It is also possible that Z = y-axis and W = x-axis 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 y-intercept 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 x-values(independent variables) and the range represents the y-values(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.

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

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 imput-output 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

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Application of Leontief Input-Output Model/Production Equation :Solving the Leontief production equation for an economy of 3 sectors (x1, x2, x3) using the Leontief Input-Output Model also know as the Production Equation. An application of Linear Systems. Please Subscribe. More Math Videos to come!