find the gradient of a line passing through point (-5,-2) and (2,3)
You asked:
Calculate the slope of the line passing through \(\left(-5, -2\right)\) and \(\left(2, 3\right)\).
MathBot Answer:
\[ \text{slope} = \frac{5}{7} \]
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: \[ \begin{aligned} \text{slope} &= \frac{y_2-y_1}{x_2-x_1} \\ &= \frac{ 3 - -2 }{ 2 - -5 } \\ &= \frac{ 5 }{ 7} \\ &= \frac{5}{7} \end{aligned} \]