Question

How to find value of x or y through given slope

Answer 1

x = 5

Step-by-step explanation

The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) is,

`m=(y_1-y_2)/(x_1-x_2)`

In this case, we know the slope of the line, and that this line passes through points (3, 1) and (x, 8),

`m=(8-1)/(x-3)\Rightarrow(7)/(2)=(7)/(x-3)`

So, we have an equation for x. Multiply both sides by (x - 3),

`\begin{gathered} (7)/(2)(x-3)=((7))/((x-3))\cdot(x-3) \\ \\ (7)/(2)(x-3)=7 \end{gathered}`

Multiply both sides by 2 and divide both sides by 7,

`\begin{gathered} (7)/(2)\cdot(2)/(7)(x-3)=7\cdot(2)/(7) \\ \\ x-3=2 \end{gathered}`

And, finally, add 3 to both sides,

`\begin{gathered} x-3+3=2+3 \\ \\ x=5 \end{gathered}`

Hence, the value of x is 5.