Slope intercept form
The slope intercept form of a line is: y = mx + b and m is the slope and b is the y-intercept
The goal of this lesson is to use the slope and a point to write the equation of a line in this form (y = mx + b)
Example #1
Given m = 2 and b = 5, write the slope intercept form
The equation is y = 2x + 5
Example #2
m =5 and (1, 6)
This time we have m, but b is missing, so we have to find b.
Since m= 5, y = mx + b becomes y = 5x + b
Now, use (1, 6) to get b
Since x = 1 and y = 6, you can replace them into the equation.
Substituting 1 for x and 6 for y gives 6 = 5×1 + b
6 = 5×1 + b is just a
linear equation that you can solve to get b
6 = 5×1 + b
6 = 5 + b
Subtract 5 from both sides
6 − 5 = 5 − 5 + b
1 = 0 + b
1 = b
Now since we have b, y = 5x + 1
Example #3
(2, 3) and (4, 9)
This time both m and b are missing, so the first thing to do is to get m and then use m and a point either (2, 3) or (4, 9) to get b
Let x
_{1} = 4, y
_{1} = 9 and x
_{2} = 2, y
_{2} = 3
m = (y
_{1} − y
_{2}) / (x
_{1} − x
_{2}) = (9 − 3)/(4 − 2 ) = 6/2 = 3
Now we can use the value for m and one point to get b as already done in example #2
Although you have two points, It does not matter which point you choose. Since both points are on the line, they will yield similar results
Choosing (2, 3), x = 2 and y = 3
Substituting 2 for x, 3 for y, and 3 for m into the equation y = mx + b we get:
3 = 3 × 2 + b
3 = 6 + b
Subtract 6 from both sides
3 − 6 = 6 − 6 + b
-3 = 0 + b
-3 = b
Now we have b = -3 and m = 3, y = 3x + -3