Question

find the slope from the pair of points

1. (-5,-4) (5,4) slope = ____ 2) (-4,-3) (-5,3) slope = ____
2. (1,-5) (3,5) slope = ____ 4) (-5,-4) (5,3) slope = ____
3. (4,-5) (-1,5) slope = ____ 6) (5,5) (-3,-1) slope = ____
4. (3,-5) (-1,5) slope = ____ 8) (-1,2) (5,-4) slope = ____
5. (-5,-2) (5,4) slope = ____ 10) (4,6) (3,3) slope = ____

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Solve for problem 1: \((-5, -4)\) and \((5, 4)\)

Let \( (x_1, y_1)=(-5, -4) \), \( (x_2, y_2)=(5, 4) \).
\( m=\frac{4 - (-4)}{5 - (-5)}=\frac{8}{10}=\frac{4}{5} \).

Step3: Solve for problem 2: \((-4, -3)\) and \((5, 3)\)

Let \( (x_1, y_1)=(-4, -3) \), \( (x_2, y_2)=(5, 3) \).
\( m=\frac{3 - (-3)}{5 - (-4)}=\frac{6}{9}=\frac{2}{3} \).

Step4: Solve for problem 3: \((1, -5)\) and \((3, 5)\)

Let \( (x_1, y_1)=(1, -5) \), \( (x_2, y_2)=(3, 5) \).
\( m=\frac{5 - (-5)}{3 - 1}=\frac{10}{2}=5 \).

Step5: Solve for problem 4: \((-5, -4)\) and \((5, 3)\)

Let \( (x_1, y_1)=(-5, -4) \), \( (x_2, y_2)=(5, 3) \).
\( m=\frac{3 - (-4)}{5 - (-5)}=\frac{7}{10} \).

Step6: Solve for problem 5: \((4, -5)\) and \((-1, 5)\)

Let \( (x_1, y_1)=(4, -5) \), \( (x_2, y_2)=(-1, 5) \).
\( m=\frac{5 - (-5)}{-1 - 4}=\frac{10}{-5}=-2 \).

Step7: Solve for problem 6: \((5, 5)\) and \((-3, -1)\)

Let \( (x_1, y_1)=(5, 5) \), \( (x_2, y_2)=(-3, -1) \).
\( m=\frac{-1 - 5}{-3 - 5}=\frac{-6}{-8}=\frac{3}{4} \).

Step8: Solve for problem 7: \((3, -5)\) and \((-1, 5)\)

Let \( (x_1, y_1)=(3, -5) \), \( (x_2, y_2)=(-1, 5) \).
\( m=\frac{5 - (-5)}{-1 - 3}=\frac{10}{-4}=-\frac{5}{2} \).

Step9: Solve for problem 8: \((-1, 2)\) and \((5, -4)\)

Let \( (x_1, y_1)=(-1, 2) \), \( (x_2, y_2)=(5, -4) \).
\( m=\frac{-4 - 2}{5 - (-1)}=\frac{-6}{6}=-1 \).

Step10: Solve for problem 9: \((-5, -2)\) and \((5, 4)\)

Let \( (x_1, y_1)=(-5, -2) \), \( (x_2, y_2)=(5, 4) \).
\( m=\frac{4 - (-2)}{5 - (-5)}=\frac{6}{10}=\frac{3}{5} \).

Step11: Solve for problem 10: \((4, 6)\) and \((3, 3)\)

Let \( (x_1, y_1)=(4, 6) \), \( (x_2, y_2)=(3, 3) \).
\( m=\frac{3 - 6}{3 - 4}=\frac{-3}{-1}=3 \).

Answer:

1. \(\frac{4}{5}\)
2. \(\frac{2}{3}\)
3. \(5\)
4. \(\frac{7}{10}\)
5. \(-2\)
6. \(\frac{3}{4}\)
7. \(-\frac{5}{2}\)
8. \(-1\)
9. \(\frac{3}{5}\)
10. \(3\)