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

Graph of the new function will be vertically stretched by 2 units.

Explanation:

A linear function is represented by the equation, y =
`(1)/(3)x+ 4`

This function has the slope =
`(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((1)/(3))x+ 4`

y =
`(a)/(3)x+4` ---------(1)

If the slope of this equation is changed to
`(2)/(3)`,

New equation of the function will be,

y =
`(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.