Question

What is the equation of the line between `(-1,12)` and `(31,16)`?

Answer 1

See a solution process below:

Explanation:

Fist, we need to determine the slope of the line. The formula for find the slope of a line is:

`m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` and `(color(red)(x_2), color(red)(y_2))` are two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(16) - color(blue)(12))/(color(red)(31) - color(blue)(-1)) = (color(red)(16) - color(blue)(12))/(color(red)(31) + color(blue)(1)) = 4/32 = 1/8`

Now, we can use this point-slope formula to write an equation for 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)(12)) = color(red)(1/8)(x - color(blue)(-1))`

`(y - color(blue)(12)) = color(red)(1/8)(x + color(blue)(1))`

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

`(y - color(blue)(16)) = color(red)(1/8)(x - color(blue)(31))`