Question

Plot the points and draw a line through them. Find the slope of the line passing through the points. $$(1,2),(2,1)$$

Short answer

The slope of the line that passes through the points \((1,2)\) and \((2,1)\) is -1.

Step-by-step solution

Plot the Points

Start by plotting the points \((1,2)\) and \((2,1)\) on a two-dimensional plane. Place a dot at the respective coordinates.

Draw the Line

Draw a line that connects these two points. This line represents the linear relationship between the two points.

Calculate the Slope

The slope of the line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \[slope =\frac{ y_2 - y_1}{x_2 - x_1}\]. Substituting our point values; \((x_1, y_1) = (1,2)\) and \((x_2, y_2) = (2,1)\), into the formula and we have: \[slope =\frac{ 1 - 2}{2 - 1} = -1\]