Enter any Number into this free calculator
$ \text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } $
How it works: Just type numbers into the boxes below and the calculator will automatically calculate the equation of line in standard, point slope and slope intercept forms.
How to enter numbers: Enter any integer, decimal or fraction. Fractions should be entered with a forward slash such as '3/4' for the fraction $$ \frac{3}{4} $$.
Determine the equation of a line passing through the points $(-2, 5)$ and $(4, -2)$.
Find the slope - intercept form of a straight line passing through the points $\left( \frac{7}{2}, 4 \right)$ and $\left(\frac{1}{2}, 1 \right)$.
If points $\left( 3, -5 \right)$ and $\left(-5, -1\right)$ are lying on a straight line, determine the slope-intercept form of the line.
How to find equation of the line determined by two points?
To find equation of the line passing through points $A(x_A, y_A)$ and $B(x_B, y_B)$ ( $ x_A \ne x_B $ ), we use formula:
$$ {\color{blue}{ y - y_A = \frac{y_B - y_A}{x_B-x_A}(x-x_A) }} $$
Example:
Find the equation of the line determined by $A(-2, 4)$ and $B(3, -2)$.
Solution:
In this example we have: $ x_A = -2,~~ y_A = 4,~~ x_B = 3,~~ y_B = -2$. So we have:
$$ \begin{aligned} y - y_A & = \frac{y_B - y_A}{x_B-x_A}(x-x_A) \\ y - 4 & = \frac{-2 - 4}{3 - (-2)}(x - (-2)) \\ y - 4 & = \frac{-6}{5}(x + 2) \end{aligned} $$
Multiply both sides with $5$ to get rid of the fractions.
$$ \begin{aligned} (y - 4)\cdot {\color{red}{ 5 }} & = \frac{-6}{5}\cdot {\color{red}{ 5 }}(x + 2)\\ 5y - 20 & = -6(x + 2)\\ 5y - 20 & = -6x - 12 \\ 5y & = -6x - 12 + 20 \\ 5y & = -6x + 8 \\ {\color{blue}{ y }} & {\color{blue}{ = -\frac{6}{5}x - \frac{8}{5} }} \end{aligned} $$
In special case (when $x_A = x_B$ the equation of the line is:
$$ {\color{blue}{ x = x_A }} $$
Example 2:
Find the equation of the line determined by $A(2, 4)$ and $B(2, -1)$.
Solution:
In this example we have: $ x_A = 2,~~ y_A = 4,$ $ x_B = 2,~~ y_B = -1$. Since $x_A = x_B$, the equation of the line is:
$$ {\color{blue}{ x = 2 }} $$
You can see from picture on the right that in special case the line is parallel to y - axis.
Note: use above calculator to check the results.
Linear equation given two points
| [1-10] /35 | Disp-Num |
[1] 2022/09/14 16:53 Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of useHomework.Comment/RequestShow the work to get answer.[2] 2022/07/20 17:47 60 years old level or over / Self-employed people / Very /
Purpose of useUsed to create risk managment algorithm.[3] 2022/07/07 23:07 20 years old level / High-school/ University/ Grad student / A little /
Purpose of useplot lines for other calculationsComment/Requestwant implicit equation for the line.[4] 2022/04/20 22:05 30 years old level / An engineer / Useful /
Purpose of useUse of formula for calculation of linear equation in program.[5] 2022/04/09 22:10 Under 20 years old / Elementary school/ Junior high-school student / Not at All /
Purpose of use Write a linear equation from a graph[6] 2020/10/20 01:31 Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of useHelping understand my homework because I had no ideaComment/RequestDecimal or fraction would be nice but it's not too hard to do the conversions.[7] 2020/10/02 23:01 20 years old level / High-school/ University/ Grad student / Very /
Purpose of uselinear regression for lab report. Time Saver![8] 2020/03/20 21:05 Under 20 years old / Elementary school/ Junior high-school student / Very /
[9] 2019/12/09 23:44 Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of useDo homework because I’m to lazy LOL X3Comment/RequestNo request, but was very useful. Thx.[10] 2019/10/23 02:27 Under 20 years old / Elementary school/ Junior high-school student / Very /
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