To convert the given equation [tex]\(3x + 2y = 5\)[/tex] into slope-intercept form, let's follow these steps:
1. Identify the given equation: The equation is [tex]\(3x + 2y = 5\)[/tex].
2. Isolate [tex]\(y\)[/tex]: We need to rearrange the equation to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
[tex]\[
3x + 2y = 5
\][/tex]
Subtract [tex]\(3x\)[/tex] from both sides to isolate the term with [tex]\(y\)[/tex]:
[tex]\[
2y = -3x + 5
\][/tex]
3. Solve for [tex]\(y\)[/tex]: Divide every term by 2 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-3}{2}x + \frac{5}{2}
\][/tex]
Now we have the equation 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 result is:
[tex]\[
y = -\frac{3}{2}x + \frac{5}{2}
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
y = -\frac{3}{2}x + \frac{5}{2}
\][/tex]
