Question

if y=2x+1 were changed to y=1/2x+1 , how would the graph of a new function compare with the first one?

Answer 1

Given: Two functions, y = 2x + 1 ............... Function 1

and
`y=(1)/(2)x+1` .................. Function 2

Both functions are of straight line.

Slope-Point form of straight line is, y = mx + c

where , m = Slope of line and c = y intercept of line.

By comparing with Slope-Point form of straight line

we get,

Both lines have same y intercept.

But slope of function 1.i.e., 2 which is more than slope of function 2.i.e.,
`(1)/(2)`

Graph of straight line depends on the value of slopes.

line with more value of slope is more steeped than line with lesser value of slope.

Therefore, Function 1 is more steeped than Function 2.

Answer 2

1) The two functions are straight lines. 2) The two functions have the same y-intercept, i.e. y=1. then both graphs cross each other at (0,1), 3) the graph of y = 2x + 1 has slope 2, while graph of y = 1/2 x + 1 has slope 1/2, then both are growing functions, but the former is steeper, this is its rate of change is greater than the rate of change of the second.