Question

Write an equation of the line parallel to y=8x-1 that contains the point (-6,2)

Answer 1

Parallel lines have the same slope so you use the 8 from the equation and plug in with your points to point slope form equation 

Answer 2

Answer:

$y=8x+50$

Step-by-step explanation:

We are looking for the same line but with a different y-intercept.

Equation of a line in its Slope–intercept form is given by:

$y=mx+b$

Where:

$m=slope\\b=y-intercept$

We know the slope which is the same of the line:

$y=8x-1$

So:

$m=8$

And we know a point:

$(x_o,y_o)=(-6,2)$

Let's find the equation of the line parallel to y=8x-1 using the data provided and the next equation:

$y-y_o=m(x-x_o)\\\\y-2=8(x-(-6))\\\\y-2=8x+48\\\\y=8x+50$

Now let's verify the result.

First, does it contains the point (-6,2)?

Evaluate the function for x=-6:

$y=8(-6)+50\\\\y=-48+50\\\\y=2$

Second, is it parallel to y=8x-1?

Try to solve the 2x2 system of equations:

$8x-y=1\hspace{3}(1)\\8x-y=-50\hspace{3}(2)$

Using elimination method:

(1) - (2)

$8x-8x-y-(-y)=1-(-51)\\\\0=-51$

The system has no solutions. Hence the lines are parallel.