Question

Solve the equation $y - 0 = \dfrac{2}{3}\left( {x - 4} \right)$.

Answer 1

To solve these types of problems convert them into linear equation form.
As given in the problem we can see two variables as complex form, and linear equation can be put in the form $ax + by + c = 0$, where the variables are $x$ and $y$, and the coefficients are $a,b$ and $c.$

Complete step-by-step solution:
Given equation is $y - 0 = \dfrac{2}{3}\left( {x - 4} \right)$ in a complex equation form.
To solve this we have to first convert into linear form.
$\Rightarrow y = \dfrac{2}{3}\left( {x - 4} \right) \\\ \Rightarrow 3y = 2\left( {x - 4} \right) \\\ \Rightarrow 3y = 2x - 8 \\\ \Rightarrow 2x - 3y = 8.$

So, we solved the equation into its linear form.
For this equation we can draw a graph, and further we can point the values on the graph as on $x - axis$ and $y - axis$.
So, as the solution to this problem, points on the graph are,
Point on the positive $x$ - axis is $\left( {4,0} \right)$.
Point on the Negative $y$ - axis is $\left( {0, - 2.67} \right)$.

Note: There are various ways of defining a line. Some important are as follows,
Slope–intercept form:
A non-vertical line can be defined by its slope $m$, and its $y -$ intercept ${y_0}$
$\Rightarrow y = mx + {y_0}.$
The line is not horizontal, it can be defined by its slope and its $x$-intercept ${x_0}$
$\Rightarrow y = m(x - {x_0}),$
These forms are deduced from the relations,
\Rightarrow m = - \dfrac{a}{b} \\\ \Rightarrow {x_0} = - \dfrac{c}{a} \\\ \Rightarrow {y_0} = - \dfrac{c}{b}. \\\