The equation [tex]f(x)= \frac{1}{2}x [/tex] is plotted on graph below (red line)
Translating [tex]f(x)[/tex] three units to the left can be done by choosing any coordinates on [tex]f(x)[/tex].
Let choose (0,0) and (2,1)
Translating 3 units on to the left gives the new coordinates (0-3, 0)=(-3,0) and (2-3, 1)=(-1, 1)
The gradient of the two functions will stay the same since the lines are parallel to each other, so m = 0.5
By joining the two coordinates (-3,0) and (-1,1), we see that the translated line crosses y-axis at 1.5
The equation of translated line is given
[tex]g(x)=0.5(x-(-3))[/tex]
[tex]g(x)=0.5(x+3)[/tex]
[tex]g(x)=0.5x+1.5[/tex]
