Slope intercept form
The slope intercept form of a line is: y = mx + b and m is the slope and b is the yintercept
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) is a point on the line
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) are two points on a line
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
Take the slope intercept form quiz below to test your knowledge of this lesson.

Oct 22, 18 04:14 PM
Take a good look at these optical illusions with geometry
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.