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In this lesson, we will learn how to derive and use the slope formula.

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From the previous lesson, we learn that the slope of a line is equals to, 'change in y' divides by 'change in x'.

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Using this definition, we can now derive the slope formula.

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Let's put the first point on the coordinate plane.

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Now,since we are deriving a formula, we can represent the x-coordinate and y-coordinate as x1, and y1 respectively.

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Let's put the second point on the plane.

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Again, we can represent the x-coordinate and y-coordinate as x2, and y2 respectively.

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Now, with these two points, we can draw a straight line and derive the slope formula from here.

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Now, imagine that we run from, x1 to x2. The change in x would be x2 minus x1.

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Alright, with this, we can replace 'change in x' with 'x2 minus x1'.

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Next, referring to the y-coordinates, when we climb up from here, the "change in y" will be, y2 minus y1.

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Now, with this, we can replace 'change in y' with 'y2 minus y1'.

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Finally, the slope is equals to, "y2 minus y1" divides by "x2 minus x1".

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Following the convention, we can represent the slope with the variable m.

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So, we now have the slope formula, m equals to, "y2 minus y1" divides by "x2 minus x1".

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Alright, let's use this formula to find the slope of this line.

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Let's view the actual coordinates for the first point. we have, x1 as 2.0, and y1 as 3.0.

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Similarly, for the second point, we have x2 as 5.0, and y2 as 6.0.

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Now, we can find the slope of this line by simply substituting these coordinates into the slope formula.

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Let me show you, substituting y2 with 6, y1 with 3, x2 with 5, and x1 with 2.

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Now, we can see that we do not need these brackets. So, let's remove them.

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Let's simplify this, negative multiply by bracket 3.0 gives negative 3.0.

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Negative multiply by bracket 2.0 gives negative 2.0.

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6.0 minus 3.0 gives positive 3.0. 5.0 minus 2.0 gives positive 3.0.

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Now, positive 3 divides by positive 3 gives positive 1.

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So, the slope of this line is positive 1.

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Let's take a look at another example. But first, let me change the coordinates of these points.

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Using this formula, we can substitute y2 with 4.0, y1 with negative 1.0, x2 with 1.0, and x1 with 6.0.

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Now, we can see that we do not need these brackets. So, let's remove them.

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Let's simplify this, negative multiply by bracket negative 1.0 gives positive 1.0

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Negative multiply by bracket 6.0 gives negative 6.0.

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4.0 plus 1.0 gives positive 5. 1.0 minus 6.0 gives negative 5.

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Now, positive 5.0 divides by negative 5.0 gives negative 1.

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So, the slope of this line is negative 1.

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That's all for this lesson, try out the practice question to test your understanding.