Math Question?

According to the table, (2, 5), (3, y) and (x, 19) are three points on the line.
In Part A, it has been found that the slope of the line, m = 7/2

For the line joining (2, 5) and (3, y), the slope is 7/2.
(y - 5)/(3 - 2) = 7/2
y - 5 = 7/2
y = 17/2

For the line joining (2, 5) and (x, 19), the slope is 7/2.
(19 - 5)/(x - 2) = 7/2
14/(x - 2) = 7/2
x - 2 = 4
x = 6

Hence, fill the table as shown in the figure below:

The line has equation y = mx + c

Using point (2, 5) and (-2, -9) we have:

5 = 2m + c...(1)

-9 = -2m + c...(2)

(1) - (2) => 4m = 14

so, m = 7/2

Hence, y = 7x/2 + c

Again, using point (2, 5) we have:

5 = 7(2)/2 + c

so, c = -2

Therefore, y = 7x/2 - 2

When x = 3, we have y = (7 x 3)/2 - 2 

so, y = 17/2 = 8.5

When y = 19, we have 19 = 7x/2 - 2

so, x = 6 

:)>

You need to find the equation of the line. The equation of the line is y=mx+c, where m is the slope. Once you find it, you can plug in x=3 into your line equation to find y. 
Similarly, to find x when y=19, plug in y=19 in the line equation. Rearrange to find x.