Question

1. points: (1, -7) (-5, 0)

Explanation:

Assuming the problem is to find the slope between the two points \((1, -7)\) and \((-5, 0)\), we use the slope formula.

Step1: Recall the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Let \((x_1, y_1)=(1, -7)\) and \((x_2, y_2)=(-5, 0)\).

Step2: Substitute the values into the formula

Substitute \(x_1 = 1\), \(y_1=-7\), \(x_2=-5\), and \(y_2 = 0\) into the slope formula:
\(m=\frac{0 - (-7)}{-5 - 1}\)

Step3: Simplify the numerator and the denominator

Simplify the numerator: \(0-(-7)=0 + 7=7\)
Simplify the denominator: \(-5 - 1=-6\)
So, \(m=\frac{7}{-6}=-\frac{7}{6}\)

(for distance):

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Let \((x_1, y_1)=(1, -7)\) and \((x_2, y_2)=(-5, 0)\)

Step2: Substitute the values into the formula

\(d=\sqrt{(-5 - 1)^2+(0 - (-7))^2}\)

Step3: Simplify the expressions inside the square root

Simplify \((-5 - 1)^2=(-6)^2 = 36\)
Simplify \((0 - (-7))^2=(7)^2=49\)
Then \(d=\sqrt{36 + 49}=\sqrt{85}\)

Answer:

The slope between the two points is \(-\frac{7}{6}\)

If the problem was of a different nature (e.g., finding the distance between the points), the solution would be different. But based on the common operation with two points, slope calculation is a likely task. The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let's also provide the distance in case that was the intended problem: