Question

Find the equation of the line that contains the point (2, 5) and parallel to y= 5/3 x - 4 *

Answer 1

Given :-

One point (2,5)

and the another line which us parallel to the line on which the point (2,5) lies

To Find:-

We have to fund the equation of line

Solution :-

If the line is parallel then their slope must be equal

$\sf\ \ m_1=m_2\\ \\ \\ \implies\sf\ In \ y=\dfrac{5}{3}x-4\\ \\ \\ \implies\sf\ m_1= \dfrac{5}{3} = m_2$

Now we have one point and slope

The equation of line be

$\boxed{\sf{\blue{ y-y_1=m(x-x_1)}}}\\ \\ \\ \sf\ \ x_1= 2\ \ ; \ \ y_1=5\ \ ; \ m=2$

$:\implies\sf\ y-5= \dfrac{5}{3}(x-2)\\ \\ \\ :\implies\sf\ 3(y-5)=5(x-2)\\ \\ \\ :\implies\sf\ 3y-15=5x-10\\ \\ \\ :\implies\sf\ 5x-3y+5=0$

$\underline{\dag{\sf{\red{\ eq^n\ = 5x-3y+5=0}}}}$