How do you find the slope of (a line passing through the points) (3, -2) and (-2, 5)?

Question

Genesis Allen · Accepted Answer

You can use the gradient (slope) formula: #m=(y_2-y_1)/(x_2-x_1)#. In this case the slope is #-7/5#.

The slope of a line is often called '#m#', and is defined as #(rise)/(run)#: the amount a line 'rises' vertically (in the #y# direction) for each unit it 'runs' horizontally (in the #x# direction). A line with a slope of 2 rises by 2 units for every unit it moves onward in #x#, while a line with a slope of #-3# falls by 3 units in #y# for each unit in #x#. A formula for this is as follows: #m=(rise)/(run) = (y_2-y_1)/(x_2-x_1)# We usually use the second point given to us in the question as #(x_2,y_2)# and the first as #(x_1,y_1)# but it doesn't matter : try the experiment for yourself of doing it the other way around, and see that you get the same answer for the slope. In this case: #m = (y_2-y_1)/(x_2-x_1) = (5-(-2))/(-2-3) = 7/(-5) = -7/5# The slope of this line is #-7/5#.

Jameson Allen · Answer

undefined To find the slope of a line passing through two points, (x₁, y₁) and (x₂, y₂), you use the formula: slope = (y₂ - y₁) / (x₂ - x₁). Substitute the coordinates of the two points into the formula to calculate the slope. So, slope = (5 - (-2)) / (-2 - 3) = (5 + 2) / (-2 - 3) = 7 / -5. Therefore, the slope of the line passing through the points (3, -2) and (-2, 5) is -7/5.