Question

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

Answer 1

ANSWER

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

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  $y=2x-14$.