Question

Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - x

a. The two equations represent lines on a graph, describe the difference in slope and y-intercept.​

Answer 1

The difference in slopes of
`f(x)\ and\ g(x)` is = 3

We can say slope of
`f(x)` is positive and 3 more than slope of
`g(x)` while slope of
`g(x)` is negative.

Difference of y-intercepts of
`f(x)\ and\ g(x)` is = -7

We can say the y-intercept of
`g(x)` is positive and 7 units above
`f(x)` while y-intercept of
`f(x)` is negative.

Explanation:

Given equation:

`f(x) =2x - 2`

`g(x) =5-x`

We need to find the difference of slopes and y-intercepts of the given equations.

The standard form of a slope intercept equation of line is given by:

`y=mx+b`

where
`m` represents slope and
`b` represents y-intercept of line.

Writing the given equations in standard form to find slope and y-intercept.

`f(x) =2x +(-2)`

Slope = 2 and y-intercept =-2

`g(x) =(-1)x+5`

Slope = -1 and y-intercept =5

The difference in slopes of
`f(x)\ and\ g(x)` is =
`2-(-1)=2+1=3`

We can say slope of
`f(x)` is positive and 3 more than slope of
`g(x)` while slope of
`g(x)` is negative.

Difference of y-intercepts of
`f(x)\ and\ g(x)` is =
`-2-5=-7`

We can say the y-intercept of
`g(x)` is positive and 7 units above
`f(x)` while y-intercept of
`f(x)` is negative.