Question

Determine the key features of a function whose value is defined as six less than triple some quantity. (2 points)

The slope is _____

the x-coordinate of the x-

Intercept is_____

and the y-coordinate of the y-intercept is_____

:: 6

:: 2

:: 3

:: 1/3

:: -6

Can y’all help me put three of these options in the right places :)

Answer 1

The slope is 3

Hence the x-coordinate of the x- intercept is 2

Hence the y-coordinate of the y- intercept is -6

Explanation:

We are to first write the statement six less than triple some quantity as an expression:

let the quantity be x

Triple the quantity to have 3x

six less than triple some quantity will be expressed 3x - 6

The required function is f(x) = 3x - 6

This is in standard form of equation of a line y = mx+c

m is the slope

c is the y-intercept

Comparing 3x - 6 with mx+c

3x = mx

3 = m

m = 3

The slope is 3

x intercept occurs at when f(x) = 0

Substitute into f(x) = 3x-6

0 = 3x-6

-3x = -6

x = 2

Hence the x-coordinate of the x- intercept is 2

y intercept occurs at when x = 0

Substitute into f(x) = 3x-6

f(x) = 3(0)-6

f(x) = -6

Hence the y-coordinate of the y- intercept is -6