Aline passes through (2,4) and (-2,2). find the value of y if (6,y) lies on the same line

y = 6, rendering the coordinate pair: (6,6)

Step-by-step explanation:

We start by writing the equation of the line that passes through two given points on the plane: and beginning with finding the slope of the segment that joints the points using the slope formula:

Let's call = (2,4), and = (-2,2). Then we have the formula for the slope:

Now that we have the slope of the line, we can find the actual equation of the line by using one of the given points, and the "point-slope" form of a line with slope "m" and going through a point - which in our case we defie as one of our given points, let's say (2, 4):

now we find what is the "y" value in such line that corresponds to an x-value of "6" to complete the coordinate pair (6, ?). For such we simply evaluate the equation above at x = 6:

Therefore, y must be "6".