Question

When analyzing three linear functions, Daniel noticed that they all intersected at the point (7, 7). What conclusion can Daniel come to about the linear function with the smallest slope?

Answer 1

For the presented problem, since Daniel noticed that they all intersected at the point (7, 7), he can conclude that the linear function that has the smallest slope is that it’d have the highest y-intercept. I am hoping that this answer has satisfied your query about this specific question.

Answer 2

Answer: The linear function with the largest slope will have the smallest y-intercept.

Step-by-step explanation: Let the three linear functions noticed by Daniel be

`A:x+y=14,\\\\B:x-y=0,\\\\\textup{and}\\C:2x-y=7.`

As shown in the attached graph, the point of intersection of these three linear functions is P(7,7).

Now, the slope-intercept forms of the three lines are

`A:y=-x+14,` slope = -1 and y-intercept = 14.

`B:y=x,` slope = 1 and y-intercept = 0.

`C:y=2x-7` slope = 2 and y-intercept = -7.

Thus, we can conclude that the linear function with the largest slope has the lowest y-intercept and vice-versa.