2017E.C \( 1^{\text {INSEMESTER MATH'S FINAL WORK SHEET GRADE } 10 \text { STUDENTS }} \) 00118631764 iven \( x=\{(2,7),(3,9),(5,13),(0,3)\} \) be a function from Z to Z defined by \( \mathrm{x})=\mathrm{ax}+\mathrm{b} \) for some integral a and b . What are the values of a and b

To find the values of \( a \) and \( b \) for the function defined by the points \( x=\{(2,7),(3,9),(5,13),(0,3)\} \), you can set up a system of equations using the linear form \( y = ax + b \). By plugging in the points into the equation, you get: 1. For \( (2, 7) \): \( 7 = 2a + b \) (Equation 1) 2. For \( (3, 9) \): \( 9 = 3a + b \) (Equation 2) 3. For \( (5, 13) \): \( 13 = 5a + b \) (Equation 3) 4. For \( (0, 3) \): \( 3 = 0a + b \) (Equation 4) From Equation 4, you immediately find \( b = 3 \). Now plug \( b \) back into the other equations: Using Equation 1: \( 7 = 2a + 3 \) leads to \( 2a = 4 \) and thus \( a = 2 \). Therefore, the values are \( a = 2 \) and \( b = 3 \). In conclusion, \( a = 2 \) and \( b = 3 \) define the function. Now you can enjoy plotting this function and seeing how it aligns with your data points!