Question

What s the equation of the line through the origin and (-2, 3)

Answer 1

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

Explanation:

Hi there!

We need to find the equation of the line that passes through the origin (the point (0,0)) and (-2,3)

There are 3 ways to write the equation of the line, although the most common way is slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

So we need to find the slope of the line first

The formula for the slope (m) calculated from two points
`(y_(2)-y_(1))/(x_(2)-x_(1))` where (
`x_(1)`,
`y_(1)`) and (
`x_(2)`,
`y_(2)`) are points

We have the needed information to calculate the slope, but let's label the values of the points to avoid any confusion

`x_(1)`=0

`y_(1)`=0

`x_(2)`=-2

`y_(2)`=3

Now substitute their values into the equation and find m

m=
`(y_(2)-y_(1))/(x_(2)-x_(1))`

m=
`(3-0)/(-2-0)`

subtract

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

so the slope of the line is
`(3)/(-2)`. It can also be rewritten as
`(-3)/(2)`

Here is the equation of the line so far:

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

we need to find b

As the equation passes through both (0,0) and (-2,3), we can use either one of them to solve for b

Let's take (0,0) for this case

Substitute 0 as x and 0 as y

0=-
`(3)/(2)`(0)+b

multiply

0=0+b

add 0 to both sides

0=b

So b is 0

The equation of the line therefore is y=
`(-3x)/(2)`

Hope this helps!