To determine To calculate: The value of m and b for the ordered pair ( 3 , − 5 ) and ( − 2 , 10 ) are the solution of the function f ( x ) = m x + b . Explanation Given Information: The provided function is f ( x ) = m x + b and the ordered pair ( 3 , − 5 ) and ( − 2 , 10 ) are the solution of the function. Formula used: Steps for substitution method: Step 1) Find a variable with coefficient 1 and solve the equation for the corresponding variable. If there is no variable with coefficient 1 , solve for any variable in either equation. Step 2) Substitute the value of the variable obtained in the step 1 into the other equation and simplify the equation to obtain an expression containing only one variable. Step 3) Find the value of the variable by solving the expression obtained in step 2 . Step 4) Substitute the value of the variable obtained in the expression obtained in step 1 . Step 5) Now, write the solution as an ordered pair. Step 6) Verify solution, by substituting the value in all the equations. Calculation: Consider the function f ( x ) = m x + b . Substitute x = 3 , y = − 5 in the equation f ( x ) = m x + b , f ( x ) = m x + b − 5 = m ( 3 ) + b − 5 = 3 m + b Substitute x = − 2 , y = 10 in the equation f ( x ) = m x + b , f ( x ) = m x + b 10 = m ( − 2 ) + b 10 = − 2 m + b Now, consider the system of equations 3 m + b = − 5 , − 2 m + b = 10 . Observe that in the equation 3 m + b = − 5 the coefficient of b is 1 . Rewrite 3 m + b = − 5 and solve for b , 3 m + b = − 5 b = − 5 − 3 m Consider the equation − 2 m + b = 10

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.1, Problem 84ES

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To calculate: The value of m and b for the ordered pair (3,−5) and (−2,10) are the solution of the function f(x)=mx+b.

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Chapter 4.1, Problem 83ES

Chapter 4.1, Problem 85ES

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