The given data is:
x 1 7 13 19
y 4 7 10 13
We can check there relationship whether it's linear or not by simply plotting the points on a scatter plot. From the attach scatter plot we can see that the it's linear relationship.
Next step is to find the slope of this data. Formula to find slope is,
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Let's take the first two points (1,4) and (7,7). So, plug in x1=1, y1=4, x2=7 and y2=7 in the above formula. Hence,
[tex] m=\frac{7-4}{7-1} [/tex]
=[tex] \frac{3}{6} [/tex]
=[tex] \frac{1}{2} [/tex]
Point slope form of a line is:
[tex] y-y_{1} =m(x-x_{1} ) [/tex]
Now we can plug in m=1/2, x1=1 and y1=4 in the above equation. So,
[tex] y-4=\frac{1}{2} (x-1) [/tex].
