Sure, to convert the given equation [tex]\( 3x + 2y = 5 \)[/tex] into slope-intercept form, which is [tex]\( y = mx + b \)[/tex], we need to solve the equation for [tex]\( y \)[/tex].
1. Start with the given equation:
[tex]\[ 3x + 2y = 5 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term:
[tex]\[ 2y = -3x + 5 \][/tex]
Here, we subtracted [tex]\( 3x \)[/tex] from both sides.
3. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{3}{2}x + \frac{5}{2} \][/tex]
We did this by dividing every term by 2 to isolate [tex]\( y \)[/tex].
Thus, the slope-intercept form of the equation is:
[tex]\[ y = -\frac{3}{2} x + \frac{5}{2} \][/tex]
Comparing this result with the given options:
- [tex]\( y = \frac{3}{2}x - \frac{5}{2} \)[/tex]
- [tex]\( y = -\frac{3}{2} x + \frac{5}{2} \)[/tex]
- [tex]\( y = -\frac{2}{3} x + \frac{5}{3} \)[/tex]
- [tex]\( y = \frac{2}{3} x - \frac{5}{3} \)[/tex]
The correct option is:
[tex]\[ y = -\frac{3}{2} x + \frac{5}{2} \][/tex]
Therefore, our choice is the second option.
