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Finding The Equation Of A Line, Given The Slope And A Point

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This video explains how to find the equation of a line, given a point and the slope of the line.

There are two ways of solving this.

One way is using the slope-intercept formula, y = mx + b

And the other way is by using the point-slope formula,  y - y_1 = m(x - x_1)

Video-Lesson Transcript

Let’s go over finding the equation of a line, given a point and the slope.

We’re going to use the slope intercept formula:

y = mx + b

For example:

(2, 5), m = -2

We’re going to solve this in two different ways.

First is the point-slope formula which is

y - y_1 = m (x - x_1)

Now, let’s substitute

y - 5 = -2 (x - 2)

Now, let’s manipulate this to get the slope intercept form

y - 5 = -2x + 4

Now, let’s isolate y by adding 5 on both sides.

y - 5 + 5 = -2x + 4 + 5
y = -2x + 9

Or the second way to solve this is to do the slope intercept form directly.

y = mx + b
y = -2x + b

Let’s solve for b by substituting the values of x and y.

5 = -2(2) + b
5 = -4 + b

Then isolate b by adding 4 on both sides

5 + 4 = -4 + 4 + b
9 = b

Now let’s write our slope intercept form

y = -2x + 9

which is the same as our first answer.

Finding the Equation of a Line