Answer:
Graph of the new function will be vertically stretched by 2 units.
Step-by-step explanation:
A linear function is represented by the equation, y = [tex]\frac{1}{3}x+ 4[/tex]
This function has the slope = [tex]\frac{1}{3}[/tex] and y-intercept = 4
If this function is stretched vertically by 'k' the the equation of the new function will be,
y = [tex]a(\frac{1}{3})x+ 4[/tex]
y = [tex]\frac{a}{3}x+4[/tex] ---------(1)
If the slope of this equation is changed to [tex]\frac{2}{3}[/tex],
New equation of the function will be,
y = [tex]\frac{2}{3}x+4[/tex] ---------(2)
Comparing equations (1) and (2),
a = 2
Therefore, graph of the new function will be stretched vertically by 2 units.
