Question

through: (-3,5) and (-4,-3)

Answer 1

To determine the equation of the line that passes through the points (-3, 5) and (-4, -3), we can follow these steps:

1. **Find the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, let \((x_1, y_1) = (-3, 5)\) and \((x_2, y_2) = (-4, -3)\).

Plugging in the values:
\[
m = \frac{-3 - 5}{-4 - (-3)} = \frac{-8}{-1} = 8
\]

2. **Use the point-slope form of the line's equation**, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points (let’s use (-3, 5)).

Substituting \(m = 8\), \(x_1 = -3\), and \(y_1 = 5\):
\[
y - 5 = 8(x + 3)
\]

3. **Simplify to find the standard form** of the equation:
\[
y - 5 = 8x + 24
\]
\[
y = 8x + 29
\]

Thus, the equation of the line that passes through the points (-3, 5) and (-4, -3) is:
\[
y = 8x + 29
\]