what is the gradient of a line with the points (2,3),(0,5)
You asked:
Calculate the slope of the line passing through \(\left(2, 3\right)\) and \(\left(0, 5\right)\).
MathBot Answer:
\[ \text{slope} = -1 \]
The slope of the line through the two distinct points \((x_1, y_1)\) and \((x_2, y_2)\), where \(x_1 \ne x_2\), is given by the formula: \[\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}\] Therefore: \[ \begin{aligned} \text{slope} &= \frac{y_2-y_1}{x_2-x_1} \\ &= \frac{ 5 - 3 }{ 0 - 2 } \\ &= \frac{ 2 }{ -2} \\ &= -1 \end{aligned} \]