To determine the slope of the line that passes through the points [tex]\((7, -5)\)[/tex] and [tex]\((3, 1)\)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here's the step-by-step solution:
1. Identify the coordinates of the two points given:
- Point 1: [tex]\((x_1, y_1) = (7, -5)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (3, 1)\)[/tex]
2. Substitute the coordinates into the slope formula to find [tex]\( m \)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Perform the subtraction in the numerator (y-coordinates):
[tex]\[
y_2 - y_1 = 1 - (-5) = 1 + 5 = 6
\][/tex]
4. Perform the subtraction in the denominator (x-coordinates):
[tex]\[
x_2 - x_1 = 3 - 7 = -4
\][/tex]
5. Divide the results obtained from steps 3 and 4 to find [tex]\( m \)[/tex]:
[tex]\[
m = \frac{6}{-4} = -\frac{6}{4} = -\frac{3}{2}
\][/tex]
Thus, the slope of the line that passes through the points [tex]\((7, -5)\)[/tex] and [tex]\((3, 1)\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex].
So, the correct answer is:
[tex]\[ m = -\frac{3}{2} \][/tex]
