Question

How do you write the point-slope form of an equation of the line that passes through the given point (-2,5), (9,5)?

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)(5) - color(blue)(5))/(color(red)(9) - color(blue)(-2)) = (color(red)(5) - color(blue)(5))/(color(red)(9) + color(blue)(2)) = 0/11 = 0`

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.

We can substitute the slope we calculated and the values from the first point in the problem line to give the formal point-slope form for the equation of the line represented by the two points in the problem.

`(y - color(red)(5)) = color(blue)(0)(x - color(red)(-2))`

`(y - color(red)(5)) = color(blue)(0)(x + color(red)(2))`

We can also substitute the slope we calculated and the values from the second point in the problem line to give the formal point-slope form for the equation of the line represented by the two points in the problem.

`(y - color(red)(5)) = color(blue)(0)(x - color(red)(9))`

If necessary, we can also reduce both these equations down to:

`y - color(red)(5) = color(blue)(0)`

Or

`y = 5`