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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

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.

X_{1} = 12, x_{2} = 19, y_{1} = 14, and y_{2} = 24

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

Slope = m = Δy/Δx = (y_{2}-y_{1})/(x_{2}-x_{1})

**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.

X_{1} = -12, x_{2} = -9, y_{1} = -4, and y_{2} = -32

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

Slope = m = Δy/Δx = (y_{2}-y_{1})/(x_{2}-x_{1})

**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.

X_{1} = 52, x_{2} = -48, y_{1} = -4, and y_{2} = -4

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

Slope = m = Δy/Δx = (y_{2}-y_{1})/(x_{2}-x_{1})

**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.