To find the slope ([tex]\( m \)[/tex]) of the line that passes through the points [tex]\((-2, 3)\)[/tex] and [tex]\((2, 11)\)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] represent the coordinates of the two points.
Given:
- Point 1: [tex]\((-2, 3)\)[/tex]
- [tex]\( x_1 = -2 \)[/tex]
- [tex]\( y_1 = 3 \)[/tex]
- Point 2: [tex]\((2, 11)\)[/tex]
- [tex]\( x_2 = 2 \)[/tex]
- [tex]\( y_2 = 11 \)[/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{11 - 3}{2 - (-2)} \][/tex]
[tex]\[ m = \frac{11 - 3}{2 + 2} \][/tex]
[tex]\[ m = \frac{8}{4} \][/tex]
[tex]\[ m = 2 \][/tex]
So, the slope of the line that passes through the points [tex]\((-2, 3)\)[/tex] and [tex]\((2, 11)\)[/tex] is [tex]\( 2 \)[/tex].
