Question

1. through: (-5, 3) and (1, -3)

Explanation:

Assuming the problem is to find the equation of the line passing through the points \((-5, 3)\) and \((1, -3)\), we can solve it as follows:

Step 1: Find the slope (\(m\))

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1=-5\), \(y_1 = 3\), \(x_2=1\), \(y_2=-3\) into the formula:
\(m=\frac{-3 - 3}{1-(-5)}=\frac{-6}{6}=- 1\)

Step 2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((-5,3)\) (we could also use \((1,-3)\)).
Substitute \(m=-1\), \(x_1=-5\), \(y_1 = 3\) into the point - slope form:
\(y - 3=-1(x+5)\)
Simplify the equation:
\(y-3=-x - 5\)
\(y=-x-5 + 3\)
\(y=-x-2\)
We can also write it in standard form \(x + y=-2\)

Answer:

The equation of the line is \(y=-x - 2\) (or \(x + y=-2\))