Slope Intercept form of line through (6, -2) w/ slope m=1/3

[mizkej]

Hi Everybody!

This is the problem I am gtrying to solve:

Write the equation ( in slope-intercept form ) of the line through (6, -2) with the slope 1/3.

I am just stuck. I see the slope and the first point but I have drawn a blank on where even to start.

Thanks in advance for your help.

[stapel_eliz]

Write the equation ( in slope-intercept form ) of the line through (6, -2) with the slope 1/3.

To learn, in general, how to find line equations when given a slope and a point (or just two points), try here.

Then note that you have the point (x₁, y₁) = (6, -2) and the slope m = 1/3. These will plug nicely into the "point-slope form": y - y₁ = m(x - x₁).

So plug the given values into the given formula, and solve for "y=" to convert point-slope form into slope-intercept form.

If you get stuck, please reply showing how far you have gotten. Thank you!

[mizkej]

I think I've got it..

1/3 (x - 6) = y-(-2)
1/3 x - 2 = y + 2
1/3 x -2 =y -2
1/3x -2 - -2 = y
1/3 x -4 = y

y = 1/3x -4!

right?

thanks so much

[stapel_eliz]

1/3 (x - 6) = y-(-2)
1/3 x - 2 = y + 2
1/3 x -2 =y -2
1/3x -2 - -2 = y
1/3 x -4 = y

How did the "y + 2" become a "y - 2"? How did "- (-2)" become "-2"?

You were fine up to here:

. . . . .(1/3)x - 2 = y + 2

Now subtract "2" from either side:

. . . . .(1/3)x - 2 - 2 = y + 2 - 2

...and simplify to get the completed answer.

[mizkej]

I took away the 2 from that side