Question

Find the slope of a line passing through the points A (-2 , -3) and B (2 , 4).

Answer 1

Answer:

• 7/4

Explanation:

Let A(-2 , -3) = (x₁ , y₁) and B(2 , 4) = (x₂ , y₂)

Then, slope of AB = (y₂ - y₁) / (x₂ - x₁)

• (4 - (-3)/(2- (-2))
• (4 + 3)/(2 + 2)
• 7/4

Hence, the slope is 7/4.

Slope of a line:

• If θ is the inclination of a line, then the value of tan θ is called the slope of a line and is denoted by m and also called gradient of line.

Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• A (-2 , -3) and B (2 , 4).

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: find:-}}}}}}}$

• Slope of the line.

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• A (-2 , -3) and B (2 , 4)

• Slope of the line =

• We know that,

$\boxed{\pink{\sf Slope \: of \: the \: line \: = \: \dfrac{y_{2} \: - \: y_{1}}{x_{2} \: - \: x_{1}}}}$

• From, A (-2 , -3) and B (2 , 4)

• Here,

• $\sf x_{1} \: = \: - \: 2$

• $\sf x_{2} \: = \: 2$

• $\sf y_{1} \: = \: - \: 3$

• $\sf y_{2} \: = \: 4$

• Substituting the values,

$\sf Slope \: of \: the \: line \: = \: \dfrac{4 \: - \: ( - \: 3)}{2 \: - \: ( - \: 2)}$

$\sf Slope \: of \: the \: line \: = \: \dfrac{4 \: + \: 3}{2 \: + \: 2}$

$\sf Slope \: of \: the \: line \: = \: \dfrac{7}{4}$

$\sf Slope \: of \: the \: line \: = \: \dfrac{\cancel{7}}{\cancel{4}}$

$\sf Slope \: of \: the \: line \: = \: 1.75$

• Therefore,

• $\underline{\boxed{\blue{\sf Slope \: of \: the \: line \: = \: \dfrac{7}{4} \: = \: 1.75.}}}$

$\Large{\bf{\purple{\mathfrak{\dag{\underline{\underline{Extra \: Information:-}}}}}}}$

Slope of a line:-

• The slope of a line is the ratio of the increment in the y co - ordinates of the line to the increment in the x co - ordinates.

$\sf Slope \: of \: a \: line \: = \: m \: = \: \tan ∅ \: = \: \dfrac{y_{2} \: - \: y_{1}}{x_{2} \: - \: x_{1}}$