To convert the given equation [tex]\(3y - 9x = -6\)[/tex] into slope-intercept form, follow these steps:
1. Isolate the [tex]\(y\)[/tex]-term on one side:
The equation is given as:
[tex]\[
3y - 9x = -6
\][/tex]
Add [tex]\(9x\)[/tex] to both sides to move the [tex]\(x\)[/tex]-term to the other side:
[tex]\[
3y = 9x - 6
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
Now, divide every term by 3 to solve for [tex]\(y\)[/tex]:
[tex]\[
\frac{3y}{3} = \frac{9x}{3} - \frac{-6}{3}
\][/tex]
Simplify each term:
[tex]\[
y = 3x - 2
\][/tex]
3. Identify the slope and y-intercept:
The slope-intercept form of a linear equation is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept. From the equation [tex]\(y = 3x - 2\)[/tex]:
- The slope ([tex]\(m\)[/tex]) is [tex]\(3\)[/tex].
- The y-intercept ([tex]\(b\)[/tex]) is [tex]\(-2\)[/tex].
Thus, the slope-intercept form of the given equation is:
[tex]\[
y = 3x - 2
\][/tex]
The slope of the line is 3, and the y-intercept is -2.
