Question

How do you graph the line that passes through the origin parallel to the line x+y=10?

Answer 1

See a solution process below:

Explanation:

The equation in the problem 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

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

Therefore, `color(red)(1)x + color(blue)(1)y = color(green)(10)` has slope:

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

A line parallel to this line will, by definition have the same slope.

We know the `y` intercept is `0` because the line passes through the origin therefore when `x = 0`, `y = 0`

We can use the slope-intercept formula to write and equation:

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 we calculated and the `y`-intercept from the point in the problem gives:

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

Or

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

We can also solve for the Standard Form:

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

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

Or

`x + y = 0`