Question

How do you write the equation in slope intercept form given (2,7) and (-4,1)?

Answer 1

See the entire solution process below:

Explanation:

First, 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)(1) - color(blue)(7))/(color(red)(-4) - color(blue)(2)) = (-6)/-6 = 1`

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.

We can substitute the slope we calculated and one of the points from the problem for `x` and `y` and then solve for `b`:

`7 = (color(red)(1) * 2) + color(blue)(b)`

`7 = 2 + color(blue)(b)`

`-color(red)(2) + 7 = -color(red)(2) + 2 + color(blue)(b)`

`5 = 0 + color(blue)(b)`

`5 = color(blue)(b)`

We can now substitute the slope and y-intercept we calculated into the formula:

`y = color(red)(1)x + color(blue)(5)`