Find the equation of the line through (3,7); parallel to 3x-y=1.

[blake322]

Find the equation of the line through (3,7); parallel to 3x-y=1.
Write the equation in standard form.

 

[Deleted member 4993]

Find the equation of the line through (3,7); parallel to 3x-y=1.
Write the equation in standard form.

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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[mmm4444bot]

Have you learned about the Point-Slope Formula?

If you know a line's slope (m) and you know the coordinates of one point on the line (x₁,y₁), then the Point-Slope Formula gives you an equation for the line:

y - y₁ = m(x - x₁)

They gave you numbers for (x₁,y₁)

You need to determine m.

Then use the formula. :cool:

 

[pka]

Find the equation of the line through (3,7); parallel to 3x-y=1.
Write the equation in standard form.

You need to realize that parallel lines have the same slope.
The line \(\displaystyle Ax+By+C=0\) where \(\displaystyle A\cdot B\ne 0\) has slope \(\displaystyle \dfrac{-A}{B}\).

If we put those two facts together we get that \(\displaystyle 4x-7y=2~\&~4x-7y=145\) are parallel lines.
Can you explain why?

If \(\displaystyle P: (p,q)\) is a point and \(\displaystyle \ell: Tx+Sy=H\) is a line then \(\displaystyle Tx+Sy=Tp+Sq\) is line parallel to \(\displaystyle \ell\) and contains \(\displaystyle P\).
Can you explain why?

 

[blake322]

thank you

thank you.

 

[dtrud]

Find the equation of the line through (3,7); parallel to 3x-y=1.
Write the equation in standard form.

Parallel Lines have the same slope.

so your second equation is y=3x+b. Substitute (3,7) into this equation and solve for b, the y-intercept of your second equation.