Question

The table below represents a linear function f(x) and the equation represents a function g (x)

part a: write a sentence to compare thw slope of thw two functions and show thw steps you used to determine the slope of f(x) and g(x).

part b: which function has a greater y-intercwpt? justify your answer ​

Answer 1

Explanation:

a). For function 'f',

Slope of a linear function passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

Slope =
`(y_2-y_1)/(x_2-x_1)`

For the function 'f' given in the table,

Slope of the linear function passing through two points (-1, -5) and (0, -1) given in the table,

Slope =
`(-5+1)/(-1-0)`

= 4

Equation of the line passing through a point (0, -1) and slope = 4 will be,

y - y' = m(x - x')

y + 1 = 4(x - 0)

y = 4x - 1

f(x) = 4x - 1

For function 'g',

Equation of the function 'g' has been given as,

g(x) = 4x + 3

By comparing this equation with the slope-intercept equation of a line,

y = mx + b

Therefore, slope of the function 'g' is,

m = 4

Since slopes of both the functions are same, linear graphs of both the functions will be parallel.

b). Equation of the function 'f' is,

f(x) = 4x - 1

y-intercept of the function = -1

Equation of function 'g',

g(x) = 4x + 3

y-intercept = 3

Therefore, function 'g' will have the greater y-intercept.