To find the slope and the [tex]$y$[/tex]-intercept of the line given by the equation [tex]\(6x + y = 2\)[/tex], we need to express the equation in the slope-intercept form, which is [tex]\(y = mx + b\)[/tex]. In this form, [tex]\(m\)[/tex] represents the slope and [tex]\(b\)[/tex] represents the [tex]$y$[/tex]-intercept.
Here are the steps to transform the equation and identify the slope and the [tex]$y$[/tex]-intercept:
1. Start with the given equation:
[tex]\[6x + y = 2\][/tex]
2. Isolate the term with [tex]\(y\)[/tex] on one side of the equation. To do this, subtract [tex]\(6x\)[/tex] from both sides:
[tex]\[y = -6x + 2\][/tex]
3. Now, the equation is in the slope-intercept form [tex]\(y = mx + b\)[/tex].
From the equation [tex]\(y = -6x + 2\)[/tex]:
- The coefficient of [tex]\(x\)[/tex] is the slope ([tex]\(m\)[/tex]). Thus, the slope of the line is [tex]\(m = -6\)[/tex].
- The constant term is the [tex]$y$[/tex]-intercept ([tex]\(b\)[/tex]). Thus, the [tex]$y$[/tex]-intercept of the line is [tex]\(b = 2\)[/tex].
In conclusion:
- The slope of the line is [tex]\(-6\)[/tex].
- The [tex]$y$[/tex]-intercept of the line is [tex]\(2\)[/tex].
