A line passes through the origin and the point (a,b). Write its equation in terms of a and b.

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nick-teal's profile pic

nick-teal | High School Teacher | (Level 3) Adjunct Educator

Posted on

We can also use y intercept form to solve this.

y = mx + b

where m is the slope, and b is the y intercept. (where x = 0, and the line crosses the y axis)

We know that the line crosses the y axis at (0,0) so that means that the y intercept is 0. We are left with

y = mx

Then we plug in (a,b) for x and y and we can solve for the slope in terms of a and b.

b = m*a

m = b/a

Our slope is b/a, so our equation isĀ 

y = (b/a) * x

violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

We can use the Two-Point form, which is:

`y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)`

where `(y_2 - y_1)/(x_2 - x_1)` is for the slope.

Set` (0,0) ` to be `(x_1,y_1) ` and `(a, b)` be `(x_2,y_2)` ,

we will have:

`y - 0 = (b - 0)/(a - 0)(x - 0)`
`y = (b)/(a)(x)`

That is it! :)

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