Question

How do you find a standard form equation for the line with point (5, 0), and whose slope is -2?

Answer 1

See the entire solution process below:

Explanation:

First, we can use the point-slope formula to write an equation for this 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 and point from the problem gives:

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

The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

We can now transform the equation we obtained above into the form as follows:

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

`y = -2x + 10`

`color(red)(2x) + y = color(red)(2x) - 2x + 10`

`2x + y = 0 + 10`

`color(red)(2)x + color(blue)(1)y = color(green)(10)`