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Igoryamba
3 years ago
15

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

Mathematics
1 answer:
sergeinik [125]3 years ago
8 0

Answer:

f(x) = x + 3

Step-by-step 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 = \frac{y_2 - y_1}{x_2 - x_1}

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

So, m = \frac{y_2 - y_1}{x_2 - x_1} becomes

m = \frac{0 - (-2)}{-3 - (-5)}

m = \frac{0 + 2}{-3 + 5}

m = \frac{2}{2}

m = 1

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

Using

m = \frac{y - y_1}{x - x_1}

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

We have

1 = \frac{y-(-2)}{x-(-5)}

1 = \frac{y+2}{x+5}

Multiply both sides by x + 5

(x+5)*1 = \frac{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

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