Question

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

Answer 1

`y = 37x - 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 (x - x 1 )`

`y - 23 = 37 (x - 19 )`

`y - 23 = 37x - 703`

`y = 37x - 703+23`

`y = 37x - 680`

Answer 2

`y=37x-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 `(19,23)`.

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

Comparing with `y=mx+c=>m=37`

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

The equation of line `l` passes through `(x_1,y_1) and` has

slope m is

`color(red)(y-y_1=m(x-x_1)`.,where,`( x_1,y_1)=(19,23) and m=37`

`:.y-23=37(x-19)`

`=>y-23=37x-703`

`=>y=37x-680`