Question

What is the point slope form of the line passing through: (5,7),(6,8)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line passing through the two points. 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)(8) - color(blue)(7))/(color(red)(6) - color(blue)(5)) = 1/1 = 1`

Now, we can use the point-slope formula to write the equation of the line. The point-slope form of a linear equation is: `(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` is a point on the line and `color(red)(m)` is the slope.

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(blue)(7)) = color(red)(1)(x - color(blue)(5))`

`y - color(blue)(7) = x - color(blue)(5)`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(blue)(8)) = color(red)(1)(x - color(blue)(6))`

`y - color(blue)(8) = x - color(blue)(6)`