Question

How do you write the equation of a line given (6,-3),(-2,-3)?

Answer 1

`y=-3`

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)(-3) - color(blue)(-3))/(color(red)(-2) - color(blue)(6)) = (color(red)(-3) + color(blue)(3))/(color(red)(-2) + color(blue)(-6)) = 0/-8 =0`

Next we can use the point-slope formula to write an equation for the line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `(color(red)(x_1, y_1))` is a point the line passes through. Substituting the slope we calculated and the values from the second point in the problem gives:

`(y - color(red)(-3)) = color(blue)(0)(x - color(red)(6))`

`(y + color(red)(3)) = 0`

`y=-3`

Answer 2

`y=-3`

Explanation:

Begin by finding the slope using the slope formula:
`m=(y_2-y_1)/(x_2-x_1)`

Let `(6,-3)->(color(red)(x_1),color(blue)(y_1))` and `(-2,-3)->(color(red)(x_2),color(blue)(y_2))`

Find the slope:

`m=color(blue)(-3-(-3))/color(red)(-2-6)=0/-8=0`

The equation of the line can be found using the point-slope formula: `y-y_1=m(x-x_1)` where `m` is the slope and `(x_1,y_1)` is a point on the function. Since we have a slope and two points (we can choose either one. I will use `(-2,-3)`), we can substitute this information like so:

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

Simplify:

`y+3=0x+0`

`y+3=0`

Write in `y=mx+b` form by isolating the `y`

`y+cancel(3-3)=0-3`

`y=-3` <-- Equation of the line

Answer 3

See a solution process below:

Explanation:

Because both of the `y` values are the same and equal to `color(red)(-3)` we know, by definition this is a horizontal line.

Horizontal lines have the form:

`y = color(red)(a)` where `a` is the value of `y` which is the same for each and every value of `x`.

Therefore, for this problem, an equation is:

`y = color(red)(-3)`