Question

Write an equation for the line in point-slope form and then convert it to standard form. through (2, 3) and (3,5)​

Answer 1

First of all We need to find the slope with the given coordinates and then write the equation in standard form...

$\tt \: (x_1,y_1)=(2,3)$

$\tt \: (x_2,y_2)=(3,5)$

Finding the slope

$\boxed{\bf\:m =\frac{ y_{2}-y_{1}}{ x_{2}-x_{1}}}$

$\sf \: m = \frac{5 - 3}{3 - 2}$

$\sf \: m = \frac{2}{1}$

$\sf \: m = 2$

Now, Write the equation using formula

$\rm \: y -y_{1} = m(x -x_{1})$

$\rm \: y - 3 = 2(x - 2)$

$\rm \: y - 3 = 2x - 4$

$\rm \: y = 2x - 4 + 3$

$\rm \: y = 2x - 1$

Move the variable to the left-hand side and change its sign

$\rm \: y - 2x = - 1$

Use the commutative property to reorder the terms

$\rm \: - 2x + y = - 1$

Change the signs on both sides of the equation

$\boxed{ \purple{ \bf2x - y = 1}}$

Answer 2

Answer:

equation of the line: 2x - y = 1

Step-by-step explanation:

Given coordinates: (2, 3) and (3,5)​

find slope of the equation:

• $\frac{y2-y1}{x2-x1}$

using the formula:

→ $\frac{5-3}{3-2}$

→ $2$ .............this is slope, also refereed as (m) in short form.

using the equation formula:

• y - y1 = m ( x - x1 )

using the formula:

→ y - 3 = 2 ( x - 2 )

→ y - 3 = 2x - 4

→ y = 2x -4 +3

→ y = 2x - 1

→ -2x + y = -1

→ (-2x + y)/-1 = -1 /-1             [ divide both sides by -1 ]

→ 2x - y = 1  .......final answer in standard form where ( Ax + By = C ) where "A" should be positive and "C" constant on the right hand side.