- All Math Calculators
- ::
- Analytic Geometry
- ::
- Two point form

This online calculator can **find** and **plot the equation** of a straight line passing through the two
points. The calculator will generate a **step-by-step explanation** on how to obtain the result.

**Result:**

The equation of the line passing through point $ A=\left(~0~,~0~\right) $ , and point $ B=\left(~100~,~100~\right) $ is:

$$ y = x $$**Explanation:**

To find equation of the line passing through points $ A(x_A,y_A) $ and $ B(x_B,y_B) $, we use formula:

$$ y - y_A~=~\frac{y_B - y_A}{x_B - x_A}(x-x_A) $$In this example we have $ x_A = 0 $ , $ y_A = 0 $ , $ x_B = 100 $ and $ y_ B = 100 $. So,

$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\ y - 0~&=~\frac{ 100 - 0 }{ 100 - 0 } \left( x - 0 \right) \\y - 0 ~&=~ 1 \left( x - 0 \right) \\y - 0 ~&=~ 1x + 0 \\y ~&=~ 1x + 0 \end{aligned} $$Share this result with others by using the link below.

You can click here to verify link or you can just copy and paste link wherever you need it.

working...

examples

example 1:ex 1:

Determine the equation of a line passing through the points $(-2, 5)$ and $(4, -2)$.

example 2:ex 2:

Find the slope - intercept form of a straight line passing through the points $\left( \frac{7}{2}, 4 \right)$
and $\left(\frac{1}{2}, 1 \right)$.

example 3:ex 3:

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.

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:

**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.

**Quick Calculator Search**

** Please tell me how can I make this better.**

221 053 781 solved problems