How do you get the point slope and slope intercept form for the point (6,2)?

Question

I need to write a point slope form and slope intercept form for the line (6,2), (1, -1). Using the first set of points, i need to write the epuations after finding the slope. Can someone please show me how to do this in detail, and maybe even how to do these types of problems in general. PLEASE! It will be sooo greatly appreciated!

Answer 1

You have 2 points, (x1,y1) and (x2,y2) and you want to find the equation of the line that goes through these points.

The first thing you want to do is find the slope.
slope is rise/run so m = (y1-y2)/(x1-x2)

For slope intercept form , y = mx + b
where m is the slope, and b is the y intercept
now that you have found the slope, you can solve for b, the y intercept by plugging in your value for m and one of the given points, either (x1,y1) or (x2,y2).

For point slope form, y - K = m(x - H)
m is the slope, and (H,K) is a point that the line passes through.
Since you have already calculated the slope, m, for the slope intercept form, you're already almost done. All you have to do is plug in the point (x1,y1) or (x2,y2). In your question, you are asked for the point slope form of just point (6,2).

Answer 2

1st, the slope of the line passing through 2 points is the difference in y-value divided by the difference in x-value, (Y2 - Y1)/(X2 - X1), so the slope of this line is
(2 - -1)/(6 - 1) = (2 + 1)/5 = 3/5
To arrive at the point-slope form, pick one of the points (say (6,2))and set up the ratio

(y - 2).... 3
-------- = -- , then
(x - 6).... 5

(y - 2) = (3/5)(x - 6)

At this point you can get rid of the slope fraction, giving

5(y - 2) = 3(x - 6), or 5y - 10 = 3x - 18, or 5y = 3x - 8

To get to the slope-intercept form, you want y alone on the left, (y = mx + b), so divide through by 5 again, giving

y = (3/5)x - 8/5 ("fractional form"), and
y = 0.6x - 1.6 ("decimal form")

You can really normalize your fractions and do your distributions any time you want, but maintaining fractional form helps me to visualize the process, and is usually exact. You don't have to worry about where to round numbers until you have your final solution.

Answer 3

m= 3/5
b= 8/5

Answer 4

slope= (y1-y2)/(x1-x2)
(-1-2)/(1-6)= -3/-5=3/5
y=mx+b
2=3/5(6)+b
2=18/5 +b
b= -8/5
y=3/5x-8/5

My bad!

Answer 5

I just want to say that yupchagee has the correct answer

Now everyone is correct :)

Answer 6

slope=(2-(-1)/(6-1)=3/5
y=(3/5)x+b
-1=(3/5)+b
-8/5=b
b=-8/5

y=3x/5-8/5