Question

A function represented by the equation y=1/3x + 4 is a graph on a coordinate plane. What will happen to the line if the slope is changed to 2/3?

Answer 1

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 = $\frac{1}{3}x+ 4$

This function has the slope = $\frac{1}{3}$ and y-intercept = 4

If this function is stretched vertically by 'k' the the equation of the new function will be,

y = $a(\frac{1}{3})x+ 4$

y = $\frac{a}{3}x+4$ ---------(1)

If the slope of this equation is changed to $\frac{2}{3}$,

New equation of the function will be,

y = $\frac{2}{3}x+4$ ---------(2)

Comparing equations (1) and (2),

a = 2

Therefore, graph of the new function will be stretched vertically by 2 units.