Question

A line passes through (10,2) and (14,-22). Write the equation of the line in standard form.

Answer 1

The equation of the line in standard form is:

`6x + y = 62`

Explanation:

Given the points

• (10,2)

• (14,-22)

Determining the slope between (10, 2) and (14, -22)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(10,\:2\right),\:\left(x_2,\:y_2\right)=\left(14,\:-22\right)`

`m=(-22-2)/(14-10)`

`m=-6`

The point-slope form of the line equation is

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

substituting the values m = -6 and the point (10, 2) in the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

`y - 2 = -6(x - 10)`

`y - 2 = -6x +60`

adding 2 to both sides

`y-2+2 = -6x + 60 + 2`

`y = -6x + 62`

We can write the equation in the standard form such as

Ax + By = C

Thus,

`y = -6x + 62`

adding -6x to both sides

`6x + y = -6x + 62 + -6x`

`6x + y = 62`

Therefore, the equation of the line in standard form is:

`6x + y = 62`