Find the slope of the line passing through the points with coordinates (-1; 6) and (3; -1).

| August 16, 2021 | education

The coordinates of the points through which the given line passes are (-1; 6) and (3; -1).
Let’s put them on the coordinate system. Let’s build a rectangle with sides parallel to the axes. Let’s mark the sides and find their lengths.
The length of the side A, parallel to the x-axis, is equal to (-1) -3 = -4 (modulo just 4).
The length of side B parallel to the y-axis is 6 – (- 1) = 7.
Let us write the equation of the straight line in general form: y = ax + b.
According to the condition, it is necessary to find the slope of the straight line, that is, the value a. It is equal to the tangent of the angle of inclination of the straight line to the x-axis, that is, as can be seen from the graph, the ratio of side B to side A. B / A = 7 / (- 4) = (- 7) / 4.
Conclusion: the straight line passes at an obtuse angle to the x-axis.



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