Question

Write an equation in standard form for the line that passes through the given points.

(0,6) and (4.0)

Answer 1

The equation of the line in standard form is
`3x+2y=12`

Explanation:

we know that

The equation of the line in standard form is

`Ax+By=C`

where

A is a positive integer

B and C are integers

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have the points

(0,6) and (4.0)

substitute the values

`m=(0-6)/(4-0)`

`m=(-6)/(4)`

`m=-(3)/(2)`

step 2

Find the equation of the line in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

we have

`m=-(3)/(2)`

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem the y-intercept is given

The y-intercept is the point (0,6)

so

`b=6`

substitute

`y=-(3)/(2)x+6`

step 3

Convert to standard form

Multiply by 2 both sides to remove the fraction

`2y=-3x+12`

Adds 3x both sides

`3x+2y=12`