We have two points on a linear function. If we determine the slope using the Slope Formula, we can write the equation of the function in a slope-intercept form. Then we can substitute one of the points into the equation and isolate the y-intercept. Our friend is correct because they have qualified the line as being a linear function. A linear function can only have one output for each input.
Our Cousin
Our cousin claims that the two points could lie on a vertical line. Let's graph an example of this situation.
On the above graph, x=2, we have infinitely many outputs. Two outputs have been marked on the graph. However, this is not a linear function. Our cousin is incorrect because they are forgetting that the line is already stated to be a linear function.
