Question

Paralell to y=4x-6 through (12,10)

Answer 1

The line that is parallel to
`y=4x-6` through
`(12,10)` is
`y=2x-14`.

Step-by-step explanation

The equation that is parallel to the line
`y=4x-6` has a slope that is equal to the slope of this line.

By comparing this equation to the general slope intercept form,

`y=mx+c`,this line has slope
`m=2`.

Hence the line parallel to this line also has slope
`m=2`.

Let
`y=mx+b` be the equation of the line parallel to the line

`y=4x-6`

We can substitute
`m=2` to obtain;

`y=2x+b`

If the line passes through the point
`(12,10)`,then this point must satisfy its equation.

We substitute
`x=12` and
`y=10` to obtain;

`10=2(12)+b`

We this equation for
`b`.

`\Rightarrow 10=24+b`

`\Rightarrow 10-24=b`

`\Rightarrow -14=b`

We substitute this value of
`b=-14` in to
`y=2x+b` to get;

`y=2x+-14`.

Hence the equation of the line that is parallel to
`y=4x-6` through
`(12,10)` is
`y=2x-14`.