Which equation represents a line which is parallel to the line y − 3 x = 1 y

Question

A. Y=-1/3x+5

B Y=-3x-6

C Y= 1/3x+4

D Y= 3x+2

Answer 1

The problem statement as given is y - 3x = 1y. That's a little strange because we could subtract y from both sides of the equation and y would disappear completely, leaving us with -3x = 0.

Perhaps the correct problem statement is y - 3x = 1. This is just a guess and so could be wrong. But it allows us to look at how to solve similar problems.

I suggest putting the problem into standard slope-intercept form. That's a good idea when answering questions involving slopes. Slope-intercept form means working on the equation to get it into a form that shows y = mx + b, where m is the slope and b is the intercept.

To do this for our equation, we can add 3x to both sides of the equation to get y = 3x + 1. We note that our slope is 3 since 3 is the coefficient on the x term when the equation is put into standard slope-intercept form.

All lines parallel to this line must have the same slope. So, all parallel lines will have a 3x term when put in standard slope-intercept form. The only answer that meets that requirement is D. y = 3x + 2.

I hope this helps.

So parallel lines have the same slope. Another favorite question involves perpendicular lines (lines that intersect at right angles). For our line with slope = 3, all perpendicular lines will have slope of -1/3. That is, for a line with slope m, all perpendicular lines will have slope equal to -1/m.

Answer 2

I'm going to assume the equation of the line is supposed to be y − 3x = 1

A line that is parallel will have the same slope. So, what is the slope of y - 3x = 1? To find out, put it in slope-Intercept format (y = mx + b) then the number in front of the "x" (the "m") will be the slope.

y − 3x = 1 [add "3x" to both sides to get:

y = 3x + 1

So, the slope is 3.

The equation that also has a slope of 3 is D. y = 3x + 2