Question

What is the slope-intercept form of the line passing through `(0, 6)` and `(3,0)`?

Answer 1

`y = -2x + 6`

Explanation:

In the slope intercept form `y = mx + b`
m = the slope ( think mountain ski slope. )
b = the y intercept ( think beginning )

The slope can be found by `( y_1 - y_2)/(x_1 - x_2)`

putting the values for the points into the equation gives

`(6-0)/(0-3)` = `6/-3`= `-2`

Putting this value for m the slope into an equation with one set of value for a point can be used to solve for b

`6 = -2(0) + b`

This gives

`6 = b`

so

`y = -2x + 6`

Answer 2

`color(red)(y) = -2color(green)(x) + 6`

Explanation:

First of all, You have to use the `color(Brown)("Point-Slope Form")` of Linear Equations to get the Slope of the line.

The Point-Slope Form of a Linear Equation is:-

`color(blue)(m) = color(Red)(y_2 - y_1)/color(Green)(x_2-x_1)`

Where `(color(green)(x_1), color(red)(y_1))` and `(color(green)(x_2), color(red)(y_2))` are the points on the line.

So, The Slope for the Required Line

`color(blue)(m) = (0-6)/(3 - 0) = -6/3 = color(Violet)(-2)`

Now, We can use the Slope - Intercept Form.

So, The Equation becomes,

`color(white)(xxx)color(red)(y) = color(blue)(m)color(green)(x) + color(SkyBlue)(c)`

`rArr color(red)(y) = -2color(green)(x) + color(SkyBlue)(c)`.

We have been told that The Line has a Point `(3,0)` on it.

So, The Co-ordinates of that Point must satisfy the Equation.

So,

`color(white)(xxx)0 = -2 xx 3 + color(skyblue)(c)`

`rArr color(skyblue)(c) - 6 = 0`

`rArr color(skyblue)(c) = 6`

So, The Final Equation is,

`color(red)(y) = -2color(green)(x) + 6`.

Hope this helps, and I really hope that my colour choice isn't too much bad.