Question

Examine the table of input (x) and output (y) values below. What is the relationship between the input and output values? Write an equation for this relationship. input (x) –1 0 1 2 3 4 5 output (y) –4 –1 2 5 8 11 14 What do you notice about the relationship between the x and y values?

Answer 1

Relationship: As the input increases by 1, the output increases by 3.

Equation: y=3x-1

~Hope this helps~

Answer 2

The relationship between the input (x) and output (y) values is linear with a constant slope of 3. The equation representing this relationship is
`\(y = 3x - 1\).`

Step-by-step explanation:

Examining the given input-output values, you can observe that each time the input (x) increases by 1, the output (y) increases by 3. This consistent pattern indicates a linear relationship between x and y. To determine the equation representing this relationship, consider the slope of the line connecting any two points on the table. In this case, the slope is 3, as for every increase of 1 in x, y increases by 3. The y-intercept, where the line crosses the y-axis, is -1, which is the initial value of y when x is 0. Thus, the equation
`\(y = 3x - 1\)` accurately models the given input-output relationship.

This linear equation
`\(y = 3x - 1\)` represents a straight line on the coordinate plane, and its slope of 3 signifies that for every unit increase in x, the corresponding y value increases by 3 units. The y-intercept of -1 indicates that when x is 0, y is -1. Overall, the observed pattern in the relationship between the x and y values is consistent with a linear equation, and the equation
`\(y = 3x - 1\)` succinctly describes this mathematical connection.