When a problem asks you to find an equation of a line that passes though (x,y) with..

[abel muroi]

When a problem asks you to find an equation of a line that passes though (x,y) with slope 1/2 or whatever..

Do you think i should consider using slope intercept form?

y = mx + b

or am i supposed to use the point slope form?

y - y₁ = m (x - x₁)

what about the linear form?

Ax + By + C = 0

or does it even matter?

the problems i usually get are sometimes vague..

 

[Deleted member 4993]

When a problem asks you to find an equation of a line that passes though (x,y) with slope 1/2 or whatever..

Do you think i should consider using slope intercept form?

y = mx + b

or am i supposed to use the point slope form?

y - y₁ = m (x - x₁)

what about the linear form?

Ax + By + C = 0

or does it even matter?

the problems i usually get are sometimes vague..

The equation of a line with slope 'm' and passing through (x₁,y₁) is:

y - y₁ = m (x - x₁) ...... because you were given a point and the slope.

 

[abel muroi]

The equation of a line with slope 'm' and passing through (x₁,y₁) is:

y - y₁ = m (x - x₁) ...... because you were given a point and the slope.

But if i were to use... y = mx + b

wouldn't it be the same thing?

I mean lets say for example i was told to find an equation of a line that passes through (1, -3) with slope -1/2

if i were to do this...

y = -1/2x + b
-3 = -1/2(1) + b
-3 = -1/2 + b
-5/2 = b

so the equation has to be y = -1/2x - 5/2

 

[ClaireWu]

But if i were to use... y = mx + b

wouldn't it be the same thing?

I mean lets say for example i was told to find an equation of a line that passes through (1, -3) with slope -1/2

if i were to do this...

y = -1/2x + b
-3 = -1/2(1) + b
-3 = -1/2 + b
-5/2 = b

so the equation has to be y = -1/2x - 5/2

Also can but more tedious

 

[Ishuda]

But if i were to use... y = mx + b

wouldn't it be the same thing?

I mean lets say for example i was told to find an equation of a line that passes through (1, -3) with slope -1/2

if i were to do this...

y = -1/2x + b
-3 = -1/2(1) + b
-3 = -1/2 + b
-5/2 = b

so the equation has to be y = -1/2x - 5/2

Of course the equation for the line can be written in any of the standard (and not so standard) forms you like. However, as Subhotosh Khan points out, it is easier to start with the point/slope form and go from there since that is what you are given. Had you been given the slope/y-intercept form it would be easier to start from that point, etc.

 

[Steven G]

But if i were to use... y = mx + b

wouldn't it be the same thing?

I mean lets say for example i was told to find an equation of a line that passes through (1, -3) with slope -1/2

if i were to do this...

y = -1/2x + b
-3 = -1/2(1) + b
-3 = -1/2 + b
-5/2 = b

so the equation has to be y = -1/2x - 5/2

For many year I used the point-slope formula but these days I like using the method you described above. It is just a matter of taste. I like the method you showed because it is in y=mx+b form right away.