Question

Determine $x$ so that $2$ is the slope of the line joining points $A(2,5)$ and $B(x,3)$.

Answer 1

Step 1:Finding the slope of line joining points $A(2,5)$ and $B(x,3)$:

Given coordinates of the line are $A(2,5)$ and$B(x,3)$, where

$x_1=2,x_2=x,y_1=5and{y}_2=3$

The slope of the line joining points $A$and $B$ , $m_1=\frac{y_2-y_1}{x_2-x_1}$

$$\begin{gathered} m_1=\frac{3-5}{x-2} \\ {m}_1=\frac{-2}{x-2} \end{gathered}$$

Step2- Finding the value of $x$ :

The slope of line joining points $A$and $B$ is $2$

$\Rightarrow m_1=2$

$$\begin{gathered} \Rightarrow \frac{-2}{x-2}=2 \\ \Rightarrow -2=-4+2x \\ \Rightarrow 2x=2 \\ \Rightarrow x=1 \end{gathered}$$

Hence the value of $x$ is $1$