Question

How do you find a standard form equation for the line with m=-3, b=0?

Answer 1

See the solution process below:

Explanation:

FIrst, we can write this equation in the 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.

Substituting the slope and y-intercept from the problem gives:

`y = color(red)(-3)x + color(blue)(0)`

We can now transform this equation into the Standard Form of a linear equation. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

`3x + y = 3x + color(red)(-3)x + color(blue)(0)`

`3x + y = 0 + color(blue)(0)`

`color(red)(3)x + color(blue)(1)y = color(green)(0)`