Question

The​ y-values

by

amount for every unit increase in​ x-values. Also, the points on the graph

be connected by a line. The function shown

a linear function.

Answer 1

It seems like you're describing the characteristics of a linear function. A linear function can be defined in the form \( y = mx + b \), where:

- \( m \) is the slope of the line, representing the amount by which the y-values change for every unit increase in the x-values (this is the rate of change).
- \( b \) is the y-intercept, which is the value of \( y \) when \( x \) is 0.

In a linear function, the relationship between \( x \) and \( y \) is constant, meaning that the difference in \( y \) for a one-unit increase in \( x \) is always the same. Therefore, when you plot the points corresponding to this function on a graph, they will form a straight line.

To summarize:

- The slope \( m \) shows how much \( y \) changes for each unit increase in \( x\).
- The points on the graph can be connected by a straight line, confirming it's a linear function.

If you have a specific linear function or additional details you'd like to discuss, please provide more information!