The table represents a linear function. X -2 -1 0 1 2 y 8 2 -4 -10 -16 <\/p>\n\n\n\n
What is the slope of the function? <\/p>\n\n\n\n
-6 <\/p>\n\n\n\n
-4 <\/p>\n\n\n\n
4 <\/p>\n\n\n\n
6<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is -6<\/strong>.<\/p>\n\n\n\n To find the slope of a linear function, we use the formula:<\/p>\n\n\n\n [ A linear function has a constant slope, meaning the rate of change between the ( x ) and ( y ) values is consistent across the table. We can calculate the slope by picking any two points from the table and applying the formula. Let’s use the points ( (-2, 8) ) and ( (-1, 2) ).<\/p>\n\n\n\n Now, calculate the slope:<\/p>\n\n\n\n [ The slope of the function is -6, which indicates that for every 1 unit increase in ( x ), the value of ( y ) decreases by 6 units. This makes sense because as you look at the table, each time ( x ) increases by 1, ( y ) decreases by 6. For example:<\/p>\n\n\n\n Thus, the function has a constant rate of change, confirming that the slope is indeed -6. The slope being negative shows that the function is decreasing as ( x ) increases.<\/p>\n","protected":false},"excerpt":{"rendered":" The table represents a linear function. X -2 -1 0 1 2 y 8 2 -4 -10 -16 What is the slope of the function? -6 -4 4 6 The Correct Answer and Explanation is : The correct answer is -6. 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\\text{slope} = \\frac{{\\text{change in } y}}{{\\text{change in } x}} = \\frac{{y_2 – y_1}}{{x_2 – x_1}}
]<\/p>\n\n\n\n\n
[
y_2 – y_1 = 2 – 8 = -6
]<\/li>\n\n\n\n
[
x_2 – x_1 = -1 – (-2) = -1 + 2 = 1
]<\/li>\n<\/ol>\n\n\n\n
\\text{slope} = \\frac{{-6}}{{1}} = -6
]<\/p>\n\n\n\n\n