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
Examples showing how to find the slope-intercept form
The goal of this lesson is to use the slope and a point on the a line to write the equation of the line in the slope-intercept form (y = mx + b).
Given m = 2 and b = 5, write the slope intercept form.
The equation is y = 2x + 5.
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
(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.
= 4, y1
= 9 and x2
= 2, y2
m = (y1
) / (x1
) = (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.
Nov 18, 20 01:20 PM
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