Question

How to find the y-intercept given `7x - 14y = 35`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(7)` to reduce the coefficients:

`(7x - 14y)/color(red)(7) = 35/color(red)(7)`

`(7x)/color(red)(7) - (14y)/color(red)(7) = 35/color(red)(7)`

`1x - 2y = 5`

This equation is now in Standard Linear Form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

`color(red)(1)x - color(blue)(2)y = color(green)(5)`

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

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Substituting gives:

`m = -color(red)(1)/color(blue)(-2) = 1/2`