The graph above represent a line. So its equation is a line equation with the following form:
y = mx + b EQUATION 1
where
m = slope
and
b = intercept with y-axis.
To find the equation of the line, we must first find the slope m. By definition, the slope m is given by:
[tex]m\text{ = }\frac{Y2\text{ - Y1}}{X2-X1}[/tex]
Here, (X1, Y1) represents the coordinates of a point A on the line. Also,
(X2,Y2) represent the coordinates of a point B on the line. That is:
A = (X1, Y1) and B = (X2,Y2)
So, if we take the points A = (1,4) = (X1, Y1) and B= (3,12) = (X2,Y2), and we substitute them in the slope equation, we have:
[tex]m\text{ = }\frac{Y2\text{ - Y1}}{X2-X1}\text{ = }\frac{12-4}{3-1}\text{ = }\frac{8}{2}\text{ = 4}[/tex]
Then, the slope of our linear function is m = 4. So our new linear equation for the graph will be:
y = mx+b = 4x + b
that is:
y = 4x + b EQUATION 2
Now let's find the y-intercept = b. For that purpose, we take any point on the graph, for example A= (X,Y) = (1,4) and we substitute it in equation 2:
4 = 4(1) + b
and resolve for b
4 = 4 + b so b = 0
then our final linear equation will be
y = 4x + 0 = 4x
In conclusion, the equation of the graph is
y = 4x
