To find the slope of a line passing through two points, we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Given the points [tex]\((-2, -3)\)[/tex] and [tex]\( (1, 1) \)[/tex]:
- [tex]\(x_1 = -2\)[/tex]
- [tex]\(y_1 = -3\)[/tex]
- [tex]\(x_2 = 1\)[/tex]
- [tex]\(y_2 = 1\)[/tex]
Substituting these values into the slope formula:
[tex]\[ \text{slope} = \frac{1 - (-3)}{1 - (-2)} \][/tex]
Next, simplify the expression inside the numerator and the denominator:
[tex]\[ \text{slope} = \frac{1 + 3}{1 + 2} \][/tex]
[tex]\[ \text{slope} = \frac{4}{3} \][/tex]
So, the slope of the line that passes through the points [tex]\((-2, -3)\)[/tex] and [tex]\( (1, 1) \)[/tex] is:
[tex]\[ \frac{4}{3} \][/tex]
