Question

Graph the line that passes through the points left parenthesis, minus, 4, comma, minus, 4, right parenthesis(−4,−4) and left parenthesis, minus, 6, comma, minus, 2, right parenthesis(−6,−2) and determine the equation of the line.
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Answer
Attempt 1 out of 2

Equation:
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Answer 1

To find the equation of the line that passes through the points \((-4, -4)\) and \((-6, -2)\), we will follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1)\) is \((-4, -4)\) and \((x_2, y_2)\) is \((-6, -2)\).

Substituting the values:
\[
m = \frac{-2 - (-4)}{-6 - (-4)} = \frac{-2 + 4}{-6 + 4} = \frac{2}{-2} = -1
\]

2. **Use the point-slope form of the equation of a line**:
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]

Using point \((-4, -4)\):
\[
y - (-4) = -1(x - (-4))
\]
Simplifying this gives:
\[
y + 4 = -1(x + 4)
\]
\[
y + 4 = -x - 4
\]
\[
y = -x - 4 - 4
\]
\[
y = -x - 8
\]

3. **Convert to slope-intercept form**:
The equation is already in slope-intercept form, which is:
\[
y = -x - 8
\]

Therefore, the equation of the line that passes through the points \((-4, -4)\) and \((-6, -2)\) is:
\[
\boxed{y = -x - 8}
\]