Question

What is the equation of the line given points (-12,0), (4,4)?

Answer 1

See a solution process below:

Explanation:

First, 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)(4) - color(blue)(0))/(color(red)(4) - color(blue)(-12)) = (color(red)(4) - color(blue)(0))/(color(red)(4) + color(blue)(12)) = 4/16 = 1/4`

Now, we can use the point-slope formula to write and 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)(0)) = color(red)(1/4)(x - color(blue)(-12))`

`y = color(red)(1/4)(x + color(blue)(12))`

We can modify this result to put the equation in slope-intercept form. 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.

`y = color(red)(1/4)(x + color(blue)(12))`

`y = (color(red)(1/4) xx x) + (color(red)(1/4) xx color(blue)(12))`

`y = color(red)(1/4)x + color(blue)(12)/(color(red)(4)`

`y = color(red)(1/4)x + color(blue)(3)`