Question

Line a can be described by the equation 3x - 4y = 8.

Write the equation of a line in slope intercept form that is parallel to line a and goes through point (24, 6).

Answer 1

Given:

Equation of a line is

`3x-4y=8`

To find:

The equation of line in slope intercept form that is parallel to line a and goes through point (24, 6).

Solution:

If a linear equation is
`ax+by+c=0`, then

`Slope=-(a)/(b)`

In the equation
`3x-4y=8`, a=3 and b=-4, thus the slope of the line is

`Slope=-(3)/(-4)`

`Slope=(3)/(4)`

We know that, slope of two parallel lines are same. So, slope of parallel line is

`m=(3)/(4)`

The parallel line passes through (24, 6) and have slope
`m=(3)/(4)`, so the equation of line is

`y-6=(3)/(4)(x-24)`

`y-6=(3)/(4)(x)-(3)/(4)(24)`

`y-6=(3)/(4)(x)-18`

Add 6 on both sides.

`y=(3)/(4)(x)-18+6`

`y=(3)/(4)(x)-12`

Therefore, the equation of parallel line in slope intercept form is
`y=(3)/(4)(x)-12`.