Question

Find the value of x if the slope of the line joining the points A(1, 3) and B(x; 6) is 1.​

Answer 1

Answer:

$\rm \: x = 4$

Explanation:

Given points,

• A(1, 3)
• B(x, 6)

Whose slope is 1

We need to find the value of x

We know that,

$\rm \longrightarrow \: slope = \dfrac{rise}{run} = \dfrac{y_2 - y_1}{x_2 - x_1}$

Where,

• $\rm x_1 = 1\: and \: y_1 = 3$ denotes the coordinates of the first point A
• And $\rm x_2 = x \: and \: y_2 = 6$ is the coordinate of second point B

Substituting the coordinates :-

$\rm \implies \:1 = \dfrac{6 - 3}{x - 1}$

$\rm \implies \:1 = \dfrac{3}{x - 1}$

$\rm \implies \:1(x - 1) = 3$

$\rm \implies \:x - 1= 3$

$\rm \implies \: x = 3 + 1$

$\rm \implies \:x = 4$

${ \underline {\rm {\therefore{ \: The \: value \: of \: x \: is \: 4}}}}$

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Formula used :

$\rm \longrightarrow \: slope = \dfrac{rise}{run} = \dfrac{y_2 - y_1}{x_2 - x_1}$

Where,

• $\rm x_1 \: and \: y_1$ denotes the coordinates of the first point A
• And $\rm x_2 \: and \: y_2$ is the coordinate of second point B