Points (2,9) and (-1,3) What is the equation of the line?

kborgeson | Middle School Teacher | (Level 2) Adjunct Educator

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Whenever you are given two points, start by naming the points.  (2, 9) becomes (x1, y1); then (-1, 3) becomes (x2, y2).  When you know which numbers you are putting into which formulas, it makes it much easier.

So then,  m =  3 - 9/ -1 - 2; This becomes m = -6/-3 = 2

Then you use the Point slope formula: y - y1 = m(x - x1)

Then use the point we named (x1,y1), which is (2, 9) and use m = 2.  Plug them into the Point slope formula.

y - 9 = 2(x - 2)

Next simplify:  y - 9 = 2x - 4

Add 9 to both sides.  y = 2x + 5  This line is now in slope intercept form and ready to be graphed.

Good luck!

enotechris | College Teacher | (Level 2) Senior Educator

Posted on

Given two points, you can always find the slope of a line. You're given 2 points (2,9) and (-1,3) with specific values, but generally a point is referred to by (x,y). Now he point slope formula is:

1)  (y - y1) = m(x - x1)

where m represents the value of the slope. Rearranging the equation gives:

2)   m = (y - y1) / (x - x1)

so if you plug in your point values, you get

3)   m = (9 - 3) / (2 - (-1))

subtracting a negative number means you change the sign to addition:

4)   m = (9 - 3) / (2 + 1)

which simplifies to

5)   m = 6 / 3

6)   m = 2

rdjack | Middle School Teacher | eNotes Newbie

Posted on

1.)  Find the slope of the line.

Use the slope formula:  (y2 - y1)/(x2 - x1)

9-3/2-(-1) =  6/3 which simplifies to 2.

2.)  Then plug the slope and one of the points (2,9) into the point-slope formula:

(y - y1) = m(x - x1)

y - 9 = 2(x - 2)

3.)  Then simplify into slope-intercept form.   y = mx + b

y - 9 = 2(x - 2)   distribute the 2

y - 9 = 2x - 4     solve for y.

+9        +9

y = 2x + 5      Equation of line in slope-intercept form.