Question

How do you find the slope of a line parallel to the graph of each equation 3x + 2y = 6?

Answer 1

See a solution process below:

Explanation:

The slope of a parallel line will have the same slope as the original line.

The equation in the problem is in Standard Linear form. 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

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

`color(red)(3)x + color(blue)(2)y = color(green)(6)`

The slope of this line is:

`m = -color(red)(3)/color(blue)(2)`

Therefore, the slope of a parallel line is `-3/2`