How to Find Slope of a Line How to Find Slope of a Line It is the ratio of change in ‘y’ when change in ‘x’. The slope of the line measures the steepness of the given line. We are using two word “rise over run”. In the slope of a line we have to follow some of the steps for finding the slope of the line. Now we will see How to Find Slope of a Line, Step1: - Simply we have to, find the difference of both the ‘x’ and ‘y’ coordinates and we have to place both the coordinates in the ratio. Step 2: - After that we have to put two points on a line. Because we are using two sets of order pair both the coordinates having values ‘x’ and ‘y’ and you have to used a subscript to distinguish between the two values ‘x’ and ‘y’. Step 3: - When a line has a negative slope then it goes down from left to right. Step 4: - When a line has a positive slope then it goes up from left to right. Step 5: - When a line has is vertical then the slope is undefined.
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The slope formula for given two points. The two points are (x1, y1) and (x2, y2), Then the slope of the line is denoted by ‘m’.
m = rise = change in y = y2 - y1 , run Where
change in x
x2 - x1
(x1 ≠ x2),
Example 1:- Find the slope of the straight line which passes through (9, 3) and (7, -8)? Solution: - slope of the straight line which passes through (9, 3) and (7, -8). Where the point as x1 = 9, y1 = 3 and x2 = 7, y2 = -8, To find the slope ‘m’ of the straight line which passes through (9, 3) and (7, -8), use the slope formula. i.e. Slope = m = y2 - y1- ; x2 - x1On putting the value of x1, y1 and x2, y2 in the given slope formula. m = -8 –3 ;
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7–9 m = -11; -2 m = -11 = 11/2, -2 After solving the equation we get the value of slope m = 11/2; Example2: - Determine if the lines are parallel, perpendicular or neither 12x + 4y = 7 and 6x +5y = 8? Solution:- When writing the first equation in the slope or we can say it as intercept form we get. 12x + 4y = 7, On further solving this equation we get Firstly subtract 12 x on both side of the equation, On subtraction 12x we get 12x + 4y – 12x = 7 -12x; After subtracting the equation we get the new equation. i.e. 4y = -12x + 7;
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