Question

How do you write a equation in slope intercept form of the line passing through the given points (0,2), (1,7)?

Answer 1

`y = color(red)(5)x + color(blue)(2)`

Explanation:

First, we must find 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)(7) - color(blue)(2))/(color(red)(1) - color(blue)(0)) = 5/1 = 5`

The point `(0, 2)` is the y-intercept.

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.

Substituting the slope we calculated and the y-intercept gives us:

`y = color(red)(5)x + color(blue)(2)`