Question

5. Which of the following linear functions has a graph which passes through points (−5,−2) and (−3,0)?

options:
A. f(x) = x – 3
B. f(x) = x + 3
C. f(x) = –x + 3
D. f(x) = –x – 3

Answer 1

Answer: B. f(x) = x + 3

Explanation:

Answer 2

`f(x) = x + 3`

Explanation:

Given

Points (−5,−2) and (−3,0)

Required

Find a linear function that passes through the given points

The question implies that we solve for the equation for the line;

First, the slope of the line must be calculated;

This is calculated as thus:

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

Where
`(x_1,y_1) = (-5,-2)\ and\ (x_2,y_2) = (-3,0)`

So,
`m = (y_2 - y_1)/(x_2 - x_1)` becomes

`m = (0 - (-2))/(-3 - (-5))`

`m = (0 + 2)/(-3 + 5)`

`m = (2)/(2)`

`m = 1`

The equation of the line can then be calculated using any of the given points;

Using

`m = (y - y_1)/(x - x_1)`

`Where\ (x_1,y_1) = (-5,-2)\ and\ m =1`

We have

`1 = (y-(-2))/(x-(-5))`

`1 = (y+2)/(x+5)`

Multiply both sides by x + 5

`(x+5)*1 = (y+2)/(x+5) * (x+5)`

`x + 5 = y + 2`

Subtract 2 from both sides

`x + 5 - 2 = y + 2 - 2`

`x + 3 = y`

`y = x + 3`

Replace y with f(x)

`f(x) = x + 3`

Hence, from the list of given options; Option B is correct