Pt Slope Form

What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1)? Y−1=611 (x−4) y+1=67 (x+4) y+1=611 (x+4) y+4=116 (x+1). The method for finding the slope from an equation will vary depending on the form of the equation in front of you. If the form of the equation is y=mx+c, then the slope (or gradient) is just m. If the equation is not in this form, try to rearrange the equation.

Video Tutorial

on Finding the Equation of a line From 2 points

• Write the equation in point-slope form of the line that passes through the given point and has the given slope. (4, -7); m = -1/4 answer choices.
• Point-Slope Form. Point-Slope Form can also be used to write the equation of a line given two points. Use the two given points to calculate the slope. Substitute the slope and one of the given points into the point-slope form. Rewrite equation in slope-intercept form if required.

Slope intercept vs Point Slope Form

There are a few different ways to find the equation of line from 2 points.

The first half of this page will focus on writing the equation in slope intercept form like example 1 below.

However, if you are comfortable using the point slope form of a line, then skip to the second part of this page because writing the equation from 2 points is easier with point slope form .

Example

Equation from 2 points using Slope Intercept Form

Find the equation of a line through the points (3,7) and (5,11)

Substitute the slope for 'm' in the slope intercept form of the equation

Substitute either point into the equation. You can use either (3,7) or (5,11)

Use our Calculator

You can use the calculator below to find the equation of a line from any two points. Just type numbers into the boxes below and the calculator (which has its own page here) will automatically calculate the equation of line in point slope and slope intercept forms

( Try this 'equation from 2 points' calculator on its own page here . )

Practice Problems

Substitute the slope for 'm' in the slope intercept form of the equation

Substitute either point into the equation. You can use either (4,5) or (8,7)

Substitute the slope for 'm' in the slope intercept equation

Substitute either point into the equation. You can use either (-6,7) or (-9,8)

$$ y = frac{1}{3}x +red{b} y = frac{1}{3}x +red{5} $$

Substitute the slope for 'm' in the slope intercept equation

Substitute either point into the equation. You can use either (-3,6) or (15,-6)

Example 2

Equation from 2 points using Point Slope Form

As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope.

The main advantage, in this case, is that you do not have to solve for 'b' like you do with slope intercept from.

Find the equation of a line through the points (3,7) and (5,11)

Point Slope Form Of A Linear Equation

Calculate the slope from the 2 points

Substitute the slope for 'm' in the point slope equation

y − y₁ = m(x −x₁)
y − y₁ = 2(x −x₁)

Substitute either point as x1, y1 in the equation. You can use either (3,7) or (5,11)

using (3,7):
y − 7 = 2(x− 3)

using (5,11):
y − 11 = 2(x − 5)

Practice Problems

Substitute the slope for 'm' in the point slope equation

Substitute either point into the equation. You can use either (4,5) or (8,7)

using (4,5):
y − 5 = ½(x − 4)

using (5,11) :
y − 11 = ½(x − 5)

Substitute the slope for 'm' in the point slope equation

Substitute either point into the equation. You can use either (-6,7) or (-9,8)

using (-6,7):
y − 7 = (x + 6)

using (-9, 8):
y − 8 = (x +9)

Point Slope Form Calculator

Substitute the slope for 'm' in the point slope equation

Substitute either point into the equation -3,6) and (15,-6)

using (-3, 6):
y − 6 = (x + 3)

using (15, -6):
y + 6 = (x − 15 )

If you read this whole page and looked at both methods (slope intercept form and point slope, you can see that it's substantially quicker to find the equation of line through 2 points by means of point slope

Linear Equations: