Question

what key feature of this graph proves that it is a linear function?
options:

• slope: the rise of 2 and the run of 5 are consistent as you look at the graph from left to right
• y - intercept: (0, 2) is part of the solution set and it is on the y - axis
• slope: the rise of 5 and the run of 2 are consistent as you look at the graph from left to right
• y - intercept: the y - intercept is above the origin at (0, 2)

Explanation:

Linear functions are defined by a constant, consistent slope (rate of change) across the entire graph, creating a straight line. The y-intercept alone does not confirm a function is linear, as non-linear functions can also have y-intercepts. For this graph, checking the slope: moving 5 units right (run = 5) results in 2 units up (rise = 2), and this rate is consistent everywhere on the line.

Answer:

Slope; the rise of 2 and the run of 5 are consistent as you look at the graph from left to right