Questions: given points. Write your answer in 15) (-2,-1) and (0,-5)

given points. Write your answer in 15) (-2,-1) and (0,-5)
Transcript text: given points. Write your answer in 15) $(-2,-1)$ and $(0,-5)$
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Solution

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Solution Steps

To find the equation of the line passing through the given points \((-2, -1)\) and \((0, -5)\), we can use the point-slope form of a line. First, calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Then, use the point-slope form \(y - y_1 = m(x - x_1)\) to find the equation of the line.

Step 1: Calculate the Slope

To find the equation of the line passing through the points \((-2, -1)\) and \((0, -5)\), we first calculate the slope \(m\) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{0 - (-2)} = \frac{-5 + 1}{2} = \frac{-4}{2} = -2 \]

Step 2: Determine the Y-Intercept

Using the slope \(m = -2\) and one of the points, say \((-2, -1)\), we can find the y-intercept \(b\) using the equation of a line \(y = mx + b\):

\[ -1 = (-2)(-2) + b \implies -1 = 4 + b \implies b = -5 \]

Step 3: Write the Equation of the Line

Now that we have both the slope \(m = -2\) and the y-intercept \(b = -5\), we can write the equation of the line in slope-intercept form:

\[ y = -2x - 5 \]

Final Answer

The equation of the line passing through the points \((-2, -1)\) and \((0, -5)\) is:

\[ \boxed{y = -2x - 5} \]

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