Question

How do you write an equation with X-intercept of -3 and y-intercept of 2?

Answer 1

See a solution process below:

Explanation:

`x`-intercept of `-3` is the same as `(-3, 0)`

`y`-intercept of `2` is the same as `(0, 2)`

First, we can 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)(2) - color(blue)(0))/(color(red)(0) - color(blue)(-3)) = (color(red)(2) - color(blue)(0))/(color(red)(0) + color(blue)(3)) = 2/3`

We can now use the slope-intercept formula to write and equation for the line. 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 given in the problem gives:

`y = color(red)(2/3)x + color(blue)(2)`