given two points on a line, how do you write the equation of the line in slope-intercept form?

Question

for example: (-4,10) (6,5)

Answer 1

1. Plot the points (same thing you've been doing since third grade; just put a dot on each one)

2. Draw a line between them

3. Get the slope of it (you should be able to do this by now. Rise over run.)

4. Continue the line until it crosses the Y boundary line thingy

5. Write the equation like you would any other one.

If you can't graph...

y-y
----
x-x

Subtract 10-5...5
Subtract -4-6...-10

5
----
-10

1
----
-2

Then use the slope and one set in an equation.
y=mx+b
10=1/-2 * -4 + b
10=2 + b
8=b

Simple enough?

Answer 2

Find the slope then use point-slope form.

Slope Formula (y2 - y1)(x2 - x1) [y2, y1 refer to y value from the first point and from the second point.]

In this case your slope would be:
(5 - 10)/(6 -(-4))

Simplify the numerator and the denominator.
-5/ 10

Reduce the fraction.
-1/2

Slope is negative one half.

Substitute one point and the slope into slope-point form.

(y - y1) = m(x - x1) [m = slope]

Substitue values.
(y - 10) = -1/2(x - (-4))
(y - 10) = -1/2(x + 4)

Distribute the negative one-half.
y - 10 = -1/2(x) - 2

Add ten to both sides.
y = -1/2(x) + 8

Answer 3

y=mx+b

WHERE

m=slope
b=the x intercept

So first you need to find the slope

(y2-y1)/(x2-x1)
=(5-10)/(6-(-4))
=(-5)/(10)
=-0.5

Then you need to find the x intecept, or "B" by substituting it into the equation using either point.

y=mx+b
y=(-0.5)x+b
(remember m=slope, so -0.5=m)


Let's use (6,5) because it seems easeir (no negative numbers)

y=mx+b
5=(-0.5)(6)+b
Now solve
5=(-3)+b
MOVE OVER 5 AND b
*switch the signs when you cross the lines!*
-b=-3+-5
-b=-8
times by -1 to find b, not -b
-b(-1)=-8(-1)
b=8

So rewrite now that you know b

y=mx+b
y=(-0.5)x+8

And you are done!