The data in the table illustrate a linear function.
x –3 0 3 6
y –6 –2 2 6
What is the slope of the linear function? Which graph represents the data?
A. Negative Start Fraction 4 over 3 End Fraction semicolon. A line passes through a graph.The line passes through the points left-parenthesis negative 3 comma negative 6 right-parenthesis left-parenthesis zero comma negative 2 right-parenthesis left-parenthesis 3 comma 2 right-parenthesis left-parenthesis 6 comma 6 right-parenthesis.
B. Negative Start Fraction 3 over 4 End Fraction semicolon. A line passes through a graph.The line passes through the points left-parenthesis negative 6 comma negative 3 right-parenthesis left-parenthesis negative 2 comma zero right-parenthesis left-parenthesis 2 comma 3 right-parenthesis left-parenthesis 6 comma 6 right-parenthesis.
C. Start Fraction 3 over 4 End Fraction semicolon. A line passes through a graph.The line passes through the points left-parenthesis negative 6 comma negative 3 right-parenthesis left-parenthesis negative 2 comma zero right-parenthesis left-parenthesis 2 comma 3 right-parenthesis left-parenthesis 6 comma 6 right-parenthesis.
D. Start Fraction 4 over 3 End Fraction semicolon. A line passes through a graph.
To find the slope of the linear function, we can use the formula:
slope = (change in y) / (change in x)
Looking at the table, we can see that when x increases by 3, y increases by 4.
So, slope = (4 - (-2)) / (3 - 0) = 6/3 = 2
Therefore, the slope of the linear function is 2.
To determine which graph represents the data, we can plot the points on each of the graphs and see which one has a line passing through all of them.
After plotting the points, we can see that graph B has a line passing through all of the points.
So, the answer is B. Negative Start Fraction 3 over 4 End Fraction semicolon. A line passes through a graph.The line passes through the points left-parenthesis negative 6 comma negative 3 right-parenthesis left-parenthesis negative 2 comma zero right-parenthesis left-parenthesis 2 comma 3 right-parenthesis left-parenthesis 6 comma 6 right-parenthesis.