Question

How do you write an equation of a line given (-2,0) and (0,6)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

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

The point `(0, 6)` is also the `y` intercept. Therefore we can use the slope-intercept formula to find an equation for the line. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

Substituting the slope we calculated and the y-intercept gives:

`y = color(red)(3)x + color(blue)(6)`

Answer 2

`y=3x+6`

Explanation:

First let's find the slope, `m`:

`m=frac(y_2-y_1)(x_2-x_1)`

`m=frac(6-0)(0-(-2))`

`m=frac(6)(2)=3`

Now, let's use the point slope formula of a line:

`y-y_1=m(x-x_1)`

and plug in `m=3` and one of the given points:

`y-0=3(x-(-2))`

`y=3x+6`