Question

How do you write an equation of a line passing through (0,2) and (-5,0)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line going through these two points. 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)(0) - color(blue)(2))/(color(red)(-5) - color(blue)(0)) = (-2)/-5 = 2/5`

We can now use the slope-intercept formula to write the 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.

We calculated the slope above. The y-intercept is `(0, 2)`. Substituting into the formula gives:

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