Question

How do you write an equation in slope-intercept form of the line that passes through the given points (3,5) and (0,4)?

Answer 1

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

Explanation:

First, we must determine the slope of the equation. 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)(4) - color(blue)(5))/(color(red)(0) - color(blue)(3)) = (-1)/-3 = 1/3`

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.

The y-intercept is one of the points given in the problem - (0, 4) or a y-intercept of `color(blue)(4)`

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

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