Question

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

Answer 1

Answer:

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: $(x_1,y_1)$ and $(x_2,y_2)$ beginning with finding the slope of the segment that joints the points using the slope formula: $slope=\frac{y_2-y_1}{x_2-x_1}$

Let's call $(x_1,y_1)$ = (2,4), and $(x_2,y_2)$ = (-2,2). Then we have the formula for the slope:

$slope=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{-2-2} =\frac{-2}{-4} =\frac{1}{2}$

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 $(x_0,y_0)$ - which in our case we defie as one of our given points, let's say (2, 4):

$y-y_0=m\,(x-x_0)\\y-4=\frac{1}{2} (x-2)\\y-4=\frac{1}{2} x-1\\y=\frac{1}{2} x-1+4\\y=\frac{1}{2} x+3$

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:

$y=\frac{1}{2} x+3\\y=\frac{1}{2} (6)+3\\y=3+3\\y=6$

Therefore, y must be "6".