First, you find out the difference between the x-coordinates
3 minus -1 = 4
Now the y-coordinates
8 minus 4 = 4
So, for every unit x changes, y changes one as well. Also, notice that they change in the same direction--if x goes up, y goes up. Therefore, you have the first half of the equation
x - y.
Now you just insert one of the given coordinates into that, and you have the second half.
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Verified answer
y = mx + b
m = slope
b = y - intercept
slope is found by subtracting the y's over the x's
8 - 4 = 4
3 - - 1 = 4
4/4 = 1 so the slope m = 1
y = x + b, to find b plug in (3, 8) for x and y and solve for b
8 = 3 + b
b = 5
equation: y = x + 5
In order to write the equation of the line (y=mx+b), we have to find the slope (m) and the y-intercept (b).
To figure out the slope, we subtract the two y's over the two x's.
8-4/3-(-1)
Simplify
8-4/3+1
4/4
Divide
1 <- slope
Now we have to find the y-intercept by plugging in the values. Let's choose (3,8) because it's easier to work with.
8=1(3)+b
Multiply
8=3+b
Subtract 3 from both sides.
5=b
So our equation is: y=1x+5 or y=x+5
(We can check this equation to make sure it is right by plugging in the second pair of points.
4=1(-1)+5
Multiply
4=-1+5
4=4
Therefore, the equation y=x+5 is correct.)
y =x+5
First, you find out the difference between the x-coordinates
3 minus -1 = 4
Now the y-coordinates
8 minus 4 = 4
So, for every unit x changes, y changes one as well. Also, notice that they change in the same direction--if x goes up, y goes up. Therefore, you have the first half of the equation
x - y.
Now you just insert one of the given coordinates into that, and you have the second half.
3 - 8 = -5
Check it with the other coordinate
-1 - 4= -5
Therefore, the equation of the line is
x - y = -5