Question

find the slope of the line that passes through the following pairs of points.
a. (5,4) and (-4,3)
b. (10,8) and (9,13)

Answer 1

$\large\underline{\sf{Solution-a}}$

Given that line passes through the points (5, 4) and (- 4, 3)

We know,

Slope of a line which passes through two points A(x₁, y₁) and B(x₂, y₂) is given by

$\boxed{\sf{ \: Slope, \: m \: = \: \frac{y_2 - y_1}{x_2 - x_1} \: }}$

So, here

$\rm \: x_1 = 5$

$\rm \: x_2 = - 4$

$\rm \: y_1 = 4$

$\rm \: y_2 = 3$

So, on substituting the values, we get

$\rm \: Slope, \: m \: = \: \dfrac{3 - 4}{ - 4 - 5}$

$\rm \: Slope, \: m \: = \: \dfrac{ - 1}{ - 9}$

$\rm\implies \:\rm \: Slope, \: m \: = \: \dfrac{1}{9}$

$\green{\large\underline{\sf{Solution-b}}}$

Given that line passes through the points (10, 8) and (9, 13)

We know,

Slope of a line which passes through two points A(x₁, y₁) and B(x₂, y₂) is given by

$\boxed{\sf{ \: Slope, \: m \: = \: \frac{y_2 - y_1}{x_2 - x_1} \: }}$

So, here

$\rm \: x_1 = 10$

$\rm \: x_2 = 9$

$\rm \: y_1 = 8$

$\rm \: y_2 = 13$

So, on substituting the values, we get

$\rm \: Slope, \: m \: = \: \dfrac{13 - 8}{9 - 10}$

$\rm \: Slope, \: m \: = \: \dfrac{5}{- 1}$

$\rm\implies \:\rm \: Slope, \: m \: = \: - 5$

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ADDITIONAL INFORMATION

1. Slope of a line is defined as the tangent of the angle which a line makes with the positive direction of x - axis measured in anti-clockwise direction and is represented by symbol m.

2. If a line is parallel to x - axis or it self x - axis, then slope is 0.

3. If a line is parallel to y - axis or it self y - axis, then slope is not defined.

4. Two lines having slope m and M are parallel iff m = M.

5. Two lines having slope m and M are perpendicular iff Mm = - 1

6. If angle is acute, then slope (m) > 0

7. If angle is obtuse, then slope (m) < 0

Answer 2

Answer:

Step-by-step explanation:

formula for slope of the line

slope = (y2-y1)/(x2-x1)

a) slope  = (3 - 4)/(-4-5)

            = -1/-9

            = 1/9  

b) slope = (13-8)/(9-10)

             = 5/-1

            = -5