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Find an equation for the line that passes through the points (-5, -4) and (1, -1).

a) y = x + 1
b) y = -x - 1
c) y = x - 1
d) y = -x + 1

1 Answer

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Final answer:

After calculating the slope of the line passing through the points (-5, -4) and (1, -1) as 0.5, and using this to write the equation of the line, none of the multiple choice answers match the derived equation y = 0.5x - 1.5. Therefore, it appears there may be an error in the provided options.

Step-by-step explanation:

To find an equation for the line that passes through the points (-5, -4) and (1, -1), first we need to calculate the slope of the line using the following formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Substituting the given points yields:

m = (-1 - (-4)) / (1 - (-5))
m = 3 / 6
m = 0.5

Now, we use the point-slope form of a line to write the equation. The point-slope form is y - y1 = m(x - x1). Let's use (-5, -4) as (x1, y1).

y - (-4) = 0.5(x - (-5))
y + 4 = 0.5(x + 5)
y + 4 = 0.5x + 2.5
y = 0.5x + 2.5 - 4
y = 0.5x - 1.5

Since none of the answer choices match exactly with our equation, we need to find an equivalent form by multiplying through by 2 to remove the fraction from the slope:

2y = x - 3
Divide through by 2 to isolate y:
y = x/2 - 3/2
y = 0.5x - 1.5

Again, this doesn't match any of the provided options, indicating a possible error in the choices.

User Nikson
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