 # Slope Examples

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## By using the line equation

Example 1

Find the slope of the line by using the equation of the line
3x + 9y + 27 = 0.

Solution

Step 1: Arrange the given line equation according to y = mx + b.

3x + 9y + 27 = 0

3x + 9y = -27

9y = -3x - 27

y = (-3x – 27)/9

Step 2: Simplify the above expression.

y = -3x/9 – 27/9

y = -x/3 – 3

y = -0.33x – 3

Step 3: Compare the above equation with y = mx + b.

y = mx + b

y = -0.33x – 3

Hence, by comparing

Slope = m = -0.33

Example 2

Find the slope of the line by using the equation of the line
-8x + 4y - 12 = 0.

Solution

Step 1: Arrange the given line equation according to y = mx + b.

-8x + 4y - 12 = 0

-8x + 4y = 12

4y = 8x + 12

y = (8x + 12)/4

Step 2: Simplify the above expression.

y = 8x/4 + 12/4

y = 4x/2 + 6/2

y = 2x + 3

Step 3: Compare the above equation with y = mx + b.

y = mx + b

y = 2x + 3

Hence, by comparing

Slope = m = 2

## By using two points method

Example 1: For positive integers

Find the slope of the line by using the given points of the line (12, 14) and (19, 24).

Solution

Step 1: Identify the given points of the line.

X1 = 12, x = 19, y1 = 14, and y2 = 24

Step 2: Take the general formula of the slope of the line.

Slope = m = Δy/Δx = (y2-y1)/(x2-x1)

Step 3: Put the given points in the formula of the equation of the line.

Slope = m = (24 - 14)/(19 - 12)

Slope = m = (10)/(7)

Slope = m = 1.43

Hence, the slope of the given points of the line is 1.43. since the value of the slope is positive so we can say that the slope is positive. It means that the person or object moves from left to right to go upward.

Example 2: For negative integers

Find the slope of the line by using the given points of the line (-12, -4) and (-9, -32).

Solution

Step 1: Identify the given points of the line.

X1 = -12, x = -9, y1 = -4, and y2 = -32

Step 2: Take the general formula of the slope of the line.

Slope = m = Δy/Δx = (y2-y1)/(x2-x1)

Step 3: Put the given points in the formula of the equation of the line.

Slope = m = (-32 – (-4))/(-9 – (-12))

Slope = m = (-32 + 4)/(-9 + 12)

Slope = m = (-28)/(3)

Slope = m = -9.33

Hence, the slope of the given points of the line is -9.33. Since the value of the slope is negative so we can say that the slope is negative. It means that the person or object moves from right to left to go downward.

Example 3: For mixed integers

Find the slope of the line by using the given points of the line (52, -4) and (-48, -4).

Solution

Step 1: Identify the given points of the line.

X1 = 52, x = -48, y1 = -4, and y2 = -4

Step 2: Take the general formula of the slope of the line.

Slope = m = Δy/Δx = (y2-y1)/(x2-x1)

Step 3: Put the given points in the formula of the equation of the line.

Slope = m = (-4 – (-4))/(-48 – (52))

Slope = m = (-4 + 4)/(-48 + 52)

Slope = m = 0/4

Slope = m = 0

Hence, the slope of the given points of the line is 0. Since the value of the slope is 0, so we can say that the slope is zero. It means that the person or object moves from right to left without moving up or down.