Points (2,9) and (-1,3)
What is the equation of the line?
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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
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.
Start with finding your slope. m = y2 - y1/ x2 -x1
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.
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.
y = 2x + 5 Equation of line in slope-intercept form.
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