To find the slope of the line defined by the points \((-1, -3)\) and \((2, 6)\), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
Let's designate:
- \((x_1, y_1) = (-1, -3)\)
- \((x_2, y_2) = (2, 6)\)
Now, substituting the values into the slope formula:
\[ m = \frac{6 - (-3)}{2 - (-1)} \]
Simplifying the expression:
-
Calculate the numerator: \[ 6 - (-3) = 6 + 3 = 9 \]
-
Calculate the denominator: \[ 2 - (-1) = 2 + 1 = 3 \]
Now substitute these values back into the formula:
\[ m = \frac{9}{3} \]
Simplifying further:
\[ m = 3 \]
Result
The slope of the line that passes through the points \((-1, -3)\) and \((2, 6)\) is \(3\).