To convert the given equation [tex]\( 2x + 3y = 9 \)[/tex] to the slope-intercept form, we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
1. Start with the given equation:
[tex]\[
2x + 3y = 9
\][/tex]
2. Isolate [tex]\( y \)[/tex] by moving the [tex]\( 2x \)[/tex] term to the other side of the equation:
[tex]\[
3y = -2x + 9
\][/tex]
3. Divide every term by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{-2}{3}x + \frac{9}{3}
\][/tex]
4. Simplify the constants:
[tex]\[
y = \frac{-2}{3}x + 3
\][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- The slope of the line [tex]\( m \)[/tex] is:
[tex]\[
-\frac{2}{3} \approx -0.6666666666666666
\][/tex]
- The y-intercept [tex]\( b \)[/tex] is:
[tex]\[
3
\][/tex]
So, the slope-intercept form of the equation is [tex]\( y = -\frac{2}{3}x + 3 \)[/tex].
- The slope of the line is:
[tex]\[
-\frac{2}{3} \approx -0.6666666666666666
\][/tex]
- The y-intercept is:
[tex]\[
3
\][/tex]
