# 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) 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 x1 = 4, y1 = 9 and x2 = 2, y2 = 3

m = (y1 − y2) / (x1 − x2) = (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

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