Answer :
To determine the slope between the points \((6, 1)\) and \((8, -4)\), we can use the formula for the slope of a line passing through two points. The formula is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
Given points:
[tex]\[ (x_1, y_1) = (6, 1) \quad \text{and} \quad (x_2, y_2) = (8, -4) \][/tex]
Let's substitute these values into the slope formula:
1. Calculate the difference in the y-coordinates (\(y_2 - y_1\)):
[tex]\[ y_2 - y_1 = -4 - 1 = -5 \][/tex]
2. Calculate the difference in the x-coordinates (\(x_2 - x_1\)):
[tex]\[ x_2 - x_1 = 8 - 6 = 2 \][/tex]
3. Now, divide the difference in the y-coordinates by the difference in the x-coordinates to find the slope:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5}{2} = -2.5 \][/tex]
Thus, the slope between the points \((6, 1)\) and \((8, -4)\) is:
[tex]\[ -2.5 \][/tex]
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
Given points:
[tex]\[ (x_1, y_1) = (6, 1) \quad \text{and} \quad (x_2, y_2) = (8, -4) \][/tex]
Let's substitute these values into the slope formula:
1. Calculate the difference in the y-coordinates (\(y_2 - y_1\)):
[tex]\[ y_2 - y_1 = -4 - 1 = -5 \][/tex]
2. Calculate the difference in the x-coordinates (\(x_2 - x_1\)):
[tex]\[ x_2 - x_1 = 8 - 6 = 2 \][/tex]
3. Now, divide the difference in the y-coordinates by the difference in the x-coordinates to find the slope:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5}{2} = -2.5 \][/tex]
Thus, the slope between the points \((6, 1)\) and \((8, -4)\) is:
[tex]\[ -2.5 \][/tex]
