# Question #c018f

May 1, 2016

y = 5x + 17

#### Explanation:

The first step here is to calculate the gradient of the line passing through the 2 given points using the $\textcolor{b l u e}{\text{ gradient formula }}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points}$

let $\left({x}_{1} , {y}_{1}\right) = \left(2 , 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , - 2\right)$

$\Rightarrow m = \frac{- 2 - 3}{1 - 2} = \frac{- 5}{- 1} = 5$

The equation of a line is $\textcolor{b l u e}{\text{ y=mx+c}}$
where m represents the gradient and c, the y-intercept.

Since the lines are parallel , then m = 5, parallel lines have equal gradients.

Partial equation is y = 5x + c, and to find c , substitute (-3 ,2) into the partial equation.

x = -3 , y =2 : $5 \times \left(- 3\right) + c = 2 \Rightarrow c = 17$

and the full equation is y = 5x + 17