Question

How do you find the slope and y intercept to sketch `7x+6y=30`?

Answer 1

See a solution process below:

Explanation:

This equation is in Standard Form for 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

`color(red)(7)x + color(blue)(6)y = color(green)(30)`

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

Substituting the values from the equation in the problem gives:

`m = -color(red)(7)/color(blue)(6)`

The `y`-intercept of an equation in standard form is: `color(green)(C)/color(blue)(B)`

Substituting the values from the equation in the problem gives:

`color(green)(30)/color(blue)(6) = 5` or `(0, 5)`