Question

How do you find a standard form equation for the line with y-intercept is 3 and slope is 1?

Answer 1

See the entire solution process below:

Explanation:

First, we have the necessary information to write the equation for the line in 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 values from the problem gives:

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

`y = 1x + 3`

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

`y - color(red)(x) = 1x - color(red)(x) + 3`

`-1x + 1y = 0 + 3`

`-1x + 1y = 3`

`-1(-1x + 1y) = -1 xx 3`

`1x - 1y = -3`

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