Question:
Use the graph to write a linear function that relates y to x
Solution:
To find the linear function that relates y and x in the above graph, we have to know that a linear function is given by the following formula:
[tex]y\text{ = mx+b}[/tex]
where m is the slope of the line and b is the y-coordinate of the y-intercept (when x = 0). Now, notice that in this case, when x = 0 then y= 2, thus we can conclude that b = 2 and:
[tex]y\text{ = mx+}2[/tex]
On the other hand, by definition, the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]
where (X1,Y1) and (X2, Y2) are any two points on the line. Take for example:
(X1,Y1) = (0,2)
(X2,Y2) = (6,10)
then, replacing this data in the equation of the slope, we obtain:
[tex]m\text{ = }\frac{10-2}{6-0}=\text{ }\frac{8}{6}[/tex]
then, using the slope obtained above, we can conclude that the equation of the linear function is:
[tex]y\text{ = }\frac{8}{6}x\text{ + 2}[/tex]
