Question

Determine x so that the slope of the line through (1,4) and (x,2) is 2 ​

Answer 1

Given that ,

• The two points are (1,4) and (x,2)
• The slope of the line is 2

We know that , the slope of line is given by

$\large \sf \fbox{m = \frac{ y_{2} - y_{1} }{x_{2} - x_{1} } }$

Thus ,

$\sf \mapsto 2 = \frac{2 - 4}{x_{2} - 1} \\ \\ \sf \mapsto 2(x_{2}) - 2 = - 2 \\ \\\sf \mapsto 2(x_{2}) = 0 \\ \\\sf \mapsto x_{2} = 0$

$\therefore \sf \underline{The \: value \: of \: x \: is \: 0}$

Answer 2

AnswEr:-

❀ Your Answer Is 0.

ExplanaTion:-

Given:-

• The coordinates (1,4) And (x,2).

• Slope of the line made by the coordinates = 2.

To Find:-

• The value of x.

Formula Used:-

$\\ \tt\longmapsto{\fbox{\fbox{ S = \dfrac{y_2-y_1}{x_2-x_1}.}}}$

Where,

• $\tt x_1\ \ And\ \ x_2$ Are x coordinates of the given points.

• $\tt y_1\ \ And\ \ y_2$ Are y coordinates of the given points.

So Here,

• $\tt x_1\ \ And\ \ x_2$ are x and 1 respectively.

• $\tt y_1\ \ And\ \ y_2$ are 2 and 4 respectively.

So lets put the values in formula:-

$\\ \tt\mapsto\dfrac{y_2-y_1}{x_2-x_1} = S.\\ \\ \tt\mapsto\dfrac{2-4}{x-1} = 2.\\ \\ \tt\mapsto-\dfrac{2}{x-1} = 2.\\ \\ \tt\mapsto -2 = 2(x-1).\\ \\ \tt\mapsto -2 = 2x -2.\\ \\ \tt\mapsto 2x = -2+2.\\ \\ \tt\mapsto 2x = 0. \\ \\ \tt\mapsto x = \dfrac{0}{2}.\\ \\ \tt\mapsto\underline{\underline {x = 0.}}$

❝$\therefore$ The required value of x is 0.❞