given the table of values,identify if it is linear or quadratic function. show your sulotion x= -3 -2 -1 0 1 y= 11 8 5 2 -1
Answer (1)
Answer:(y = -3x + 2)Step-by-step explanation:To determine whether the function represented by the given table of values is linear or quadratic, we can analyze the relationship between the ( x ) and ( y ) values.Given Values- ( x = -3, -2, -1, 0, 1 \)- ( y = 11, 8, 5, 2, -1 \)Step 1: Calculate the First DifferencesTo check if the function is linear, we first calculate the differences between consecutive ( y )-values.- For ( x = -3 ) and ( x = -2 ): 8 - 11 = -3 - For ( x = -2 ) and ( x = -1 ): 5 - 8 = -3 - For ( x = -1 ) and ( x = 0 ): 2 - 5 = -3 - For ( x = 0 ) and \( x = 1 ): -1 - 2 = -3 First Differences SummaryThe first differences are:- ( -3, -3, -3, -3 )Since the first differences are constant (all equal to -3), this indicates that the relationship between ( x ) and ( y ) is linear.Step 2: Determine the Equation of the Linear FunctionSince we know it's linear, we can find the equation in the form ( y = m x + b \), where ( m ) is the slope.1. Find the Slope ( m ): The slope can be calculated from the first differences: m = {change in } y {change in } x = -3 / 1 = -3 2. Using a Point to Find ( b ): We can substitute one of the points to find ( b ). Let's use the point (0, 2): 2 = -3(0) + b \implies b = 2 Final EquationThus, the equation of the linear function is:y = -3x + 2ConclusionSince we have verified that the first differences are constant, we can confidently conclude that the function represented by the table of values is a linear function. To summarize:- The function is linear.- The equation of the function is ( y = -3x + 2 ).
