Find the slopes of the lines passing through the given points(2) P (-3, 1) , Q (5, -2)
2. Find the slopes of the lines passing through the given points(2) P (-3, 1) , Q (5, -2)
Answer:-
P (–3, 1) , Q (5, –2)
Slope = [frac{y_2 – y_1}{x_2 – x_1} = frac{- 2 – 1}{5 – left( – 3 right)} = frac{- 3}{8}]
Explanation:-
The problem provides us with two points in a 2-dimensional space, namely point P and point Q. The coordinates of point P are (-3, 1), which means that it is located 3 units to the left of the origin (0,0) and 1 unit above the origin. Similarly, the coordinates of point Q are (5, -2), which means that it is located 5 units to the right of the origin and 2 units below the origin.
The problem asks us to find the slope of the line passing through points P and Q. The slope of a line is defined as the change in y divided by the change in x between any two points on the line. Mathematically, this can be expressed as:
[slope = frac{y_2 – y_1}{x_2 – x_1}]
Here, (x1, y1) and (x2, y2) are any two points on the line. We can use the coordinates of points P and Q to find the slope of the line passing through them as follows:
[slope = frac{-2 – 1}{5 – (-3)}]
Here, we have substituted the coordinates of P and Q into the slope formula. Simplifying the expression, we get:
[slope = frac{-3}{8}]
This tells us that the slope of the line passing through points P and Q is -3/8.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)