# What is the equation of the line passing through the point (19, 23) and parallel to the line y= 37x + 29?

Mar 23, 2018

$y = 37 x - 680$

#### Explanation:

Since the y= 37x + 29 's slope is 37, thus our line is also has the same slope.

m1=m2= 37

using point slope equation, y-y1 = m(x-x1)

$y - y 1 = m \left(x - x 1\right)$

$y - 23 = 37 \left(x - 19\right)$

$y - 23 = 37 x - 703$

$y = 37 x - 703 + 23$

$y = 37 x - 680$

Mar 23, 2018

$y = 37 x - 680$

#### Explanation:

We know that, if the slope of the line ${l}_{1}$ is ${m}_{1}$ and the slope of the line ${l}_{2}$is ${m}_{2}$ then color(red)(l_1////l_2<=>m_1=m_2 (parallel lines)

The line $l$ passes through $\left(19 , 23\right)$.

Line $l$ is parallel to $y = 37 x + 29$

Comparing with $y = m x + c \implies m = 37$

So, the slope of the line $l$ is $m = 37$

The equation of line $l$ passes through $\left({x}_{1} , {y}_{1}\right) \mathmr{and}$ has

slope m is

color(red)(y-y_1=m(x-x_1).,where,$\left({x}_{1} , {y}_{1}\right) = \left(19 , 23\right) \mathmr{and} m = 37$

$\therefore y - 23 = 37 \left(x - 19\right)$

$\implies y - 23 = 37 x - 703$

$\implies y = 37 x - 680$