Question

Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line

Answer 1

An equation in standard form for the line is:

`(5)/(2)x-y=-4`

Explanation:

Given the points

• (-2, -1) and (0, 4)

The slope between two points

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)`

`m=(4-\left(-1\right))/(0-\left(-2\right))`

`m=(5)/(2)`

Writing the equation in point-slope form

As the point-slope form of the line equation is defined by

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

Putting the point (-2, -1) and the slope m=1 in the line equation

`y-\left(-1\right)=(5)/(2)\left(x-\left(-2\right)\right)`

`y+1=(5)/(2)\left(x+2\right)`

`y=(5)/(2)x+4`

Writing the equation in the standard form form

As we know that the equation in the standard form is

`Ax+By=C`

where x and y are variables and A, B and C are constants

so

`y=(5)/(2)x+4`

`(5)/(2)x-y=-4`

Therefore, an equation in standard form for the line is:

`(5)/(2)x-y=-4`