Find an equation of the line parallel to the line y = 2x - 3 passing...

[abel muroi]

An equation of the line parallel to the line y = 2x - 3 passing through the point (k, 1) is


A. y = kx - 1

B. y = 2x + 1

C. y = 2(x -k) + l

D. y = (k - 2)x + (1 - 3)


This stuff is usually easy for me, but the (k, 1) threw me off a bit.

I think the answer is B since the rest of the option seem like nonsense to me.

Is B the correct answer?

 

[ksdhart]

I'd be inclined to break the problem down into its component parts. You're asked to find an equation of a line that fits two criteria: It must be parallel to the line y = 2x - 3, and it must pass through the point (k, 1). There's no bounds given for k, so that means it must hold true of all values of k. What do each of the possible answers look like when, say, k = 1? Are there any that are not parallel to the given line? Do any of them pass through the point (1, 1)? Now let k = 2, and repeat. What do you notice?

 

[Ishuda]

An equation of the line parallel to the line y = 2x - 3 passing through the point (k, 1) is


A. y = kx - 1

B. y = 2x + 1

C. y = 2(x -k) + l

D. y = (k - 2)x + (1 - 3)


This stuff is usually easy for me, but the (k, 1) threw me off a bit.

I think the answer is B since the rest of the option seem like nonsense to me.

Is B the correct answer?

See, for example,
http://cs.selu.edu/~rbyrd/math/equations/

The Point-Slope Form of the Equation of a Line
​

The equation of a line with slope m and passing through
the point ( x₁, y ₁) is given by,
​

y - y ₁ = m ( x - x₁ )
​

where m is the slope and ( x₁, y ₁) is the point given.

First, rearrange to
y = m ( x - x₁ ) + y ₁
Then, what is the point given and what is m.

 

[pka]

An equation of the line parallel to the line y = 2x - 3 passing through the point (k, 1) is

Always rewrite the line in standard form.
\(\displaystyle Ax+By+C=0\) is standard form.

The line \(\displaystyle \bf{Ax+By-(Ax_0+By_0)=0}\) is parallel to the given line through \(\displaystyle \bf{(x_0,y_0)}\).

 

[Ishuda]

Always rewrite the line in standard form.
\(\displaystyle Ax+By+C=0\) is standard form.

The line \(\displaystyle \bf{Ax+By-(Ax_0+By_0)=0}\) is parallel to the given line through \(\displaystyle \bf{(x_0,y_0)}\).

pka,

Just curious. Why do you say "Always rewrite the line in standard form." when the original line is written in a slope-intercept form and none of the choices are in standard form [two are in slope-intercept form and two are in a mixed point-slope and slope-intercept form].

 

[pka]

Just curious. Why do you say "Always rewrite the line in standard form." when the original line is written in a slope-intercept form and none of the choices are in standard form [two are in slope-intercept form and two are in a mixed point-slope and slope-intercept form].

It is purely an educational thing. I wanted students to get accustomed to thinking in that form.
One can look at the Ax+By+C=0 form and read off the slope, the intercepts, write parallels and perpendiculars.