Just like there is more than one way to peal an onion, there are several ways to write the equation of a line.

1. Pt Slope Formula Excel
2. Pt Slope Formula Equation
3. Pt Slope Formula
4. Slope Of A Logarithmic Line
5. Pt Slope Formula

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Ultimately, it comes down to preference, but in my humble opinion, there is one method that is far better than the rest: Point Slope Form!

The Point-Slope equation is specifically designed to handle the trickiest type of questions, namely, how do you write an equation given two points?

1. First, we take our two points and find the slope.
2. Next, we pick one of our two given points, and the slope we just found, and plug them into the point-slope form formula.
3. Done!

Remember, slope represents the steepness or the rate of change of our linear equation.

In fact, this method is so straightforward, that you will find writing linear equations super easy!

And through this lesson, we will discover that the point-slope form definition is really just an extension of our beloved slope formula.

It’s true! All we have to do is a little rearranging, as Math Is Fun so fittingly states, and we will see that point slope form is just the slope formula in disguise.

But the excitement continues…

2012.com This Quiz: 12 posible Whether they The other The other you www.om) This Question: 1 pt Write a slope-intercept equation for a line passing through the point (4. 2) that is parallel to the The equation of the parallel line is (Simplify your answer. Type your answer in slope. The reason this equation is called the point-slope form is very obvious. The equation only contains the slope and the fixed point on the straight line as constants, so it is called point-slope form. Sample Problems on Point-slope Equation. Problem 1: Find the equation of the straight line with slope 3 and passing through (-1, 5).

… did you know that the point-slope form helps us approximate other points on a curve (i.e., linear approximation) and is also called a first-degree Taylor polynomial?

What?

Yep, this little formula is used in calculus to find the equation of a tangent line to a curve and helps us to represent a function as an infinite sum of terms.

And no matter where you are on your mathematical journey, the idea that Algebra and Calculus are intrinsically connected is just plain cool!

Here are a few examples just to give you a taste of what we will be doing in this lesson.

Seven Point-Slope Form Examples

Find the y-intercept with slope and point

Write an equation of a line given the y intercept and another point

Using y-y1=m(x-x1) to write the equation of a line

Find the y intercept given two points

Use y=m(x-x1) + y1 to write the equation of the line

Given the Point (4,5) and Slope of 6, find y when x=24

So, together we are going to learn how to:

1. Write the equation of a line using point-slope form.
2. Represent equations from point slope form to slope intercept form.
3. Represent equations from point slope form to standard form.
4. Write equations of parallel lines and perpendicular lines by finding the line that passes through a point and has either parallel slope or perpendicular slope to the graph of a given equation.

Point Slope Form – Video

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First, let's see it in action. Here are two points (you can drag them) and the equation of the line through them. Explanations follow.

The Points

We use Cartesian Coordinates to mark a point on a graph by how far along and how far up it is:

Example: The point (12,5) is 12 units along, and 5 units up

Steps

There are 3 steps to find the Equation of the Straight Line :

• 1. Find the slope of the line
• 2. Put the slope and one point into the 'Point-Slope Formula'
• 3. Simplify

Step 1: Find the Slope (or Gradient) from 2 Points

What is the slope (or gradient) of this line?

We know two points:

• point 'A' is (6,4) (at x is 6, y is 4)
• point 'B' is (2,3) (at x is 2, y is 3)

The slope is the change in height divided by the change in horizontal distance.

Looking at this diagram ...

Slope m = change in ychange in x = y_A − y_Bx_A − x_B

In other words, we:

• subtract the Y values,
• subtract the X values
• then divide

Like this:

m = change in ychange in x = 4−36−2 = 14 = 0.25

It doesn't matter which point comes first, it still works out the same. Try swapping the points:

m = change in ychange in x = 3−42−6 = −1−4 = 0.25

Same answer.

Step 2: The 'Point-Slope Formula'

Now put that slope and one point into the 'Point-Slope Formula'

Start with the 'point-slope' formula (x₁ and y₁ are the coordinates of a point on the line):

Pt Slope Formula Excel

y − y₁ = m(x − x₁)

We can choose any point on the line for x₁ and y₁, so let's just use point (2,3):

y − 3 = m(x − 2)

We already calculated the slope 'm':

m = change in ychange in x = 4−36−2 = 14

And we have:

y − 3 = 14(x − 2)

That is an answer, but we can simplify it further.

Step 3: Simplify

And we get:

Which is now in the Slope-Intercept (y = mx + b) form.

Check It!

Let us confirm by testing with the second point (6,4):

y = x/4 + 5/2 = 6/4 + 2.5 = 1.5 + 2.5 = 4

Yes, when x=6 then y=4, so it works!

Another Example

Example: What is the equation of this line?

Start with the 'point-slope' formula:

y − y₁ = m(x − x₁)

Put in these values:

Pt Slope Formula Equation

• x₁ = 1
• y₁ = 6
• m = (2−6)/(3−1) = −4/2 = −2

And we get:

Pt Slope Formula

y − 6 = −2(x − 1)

Simplify to Slope-Intercept (y = mx + b) form:

y − 6 = −2x + 2

y = −2x + 8

DONE!

The Big Exception

Slope Of A Logarithmic Line

The previous method works nicely except for one particular case: a vertical line:

Pt Slope Formula