Question

how to find value of x or y through given slope

Answer 1

ANSWER

x = 5

EXPLANATION

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

$m=\frac{y_1-y_2}{x_1-x_2}$

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

$m=\frac{8-1}{x-3}\Rightarrow\frac{7}{2}=\frac{7}{x-3}$

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

$\begin{gathered} \frac{7}{2}(x-3)=\frac{(7)}{(x-3)}\cdot(x-3) \\ \\ \frac{7}{2}(x-3)=7 \end{gathered}$

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

$\begin{gathered} \frac{7}{2}\cdot\frac{2}{7}(x-3)=7\cdot\frac{2}{7} \\ \\ x-3=2 \end{gathered}$

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.