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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

2 Answers

5 votes

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

Explanation:

User Tho Ho
by
8.4k points
4 votes

Answer:


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

User Nefariis
by
7.8k points

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