Sure, let's find the slope-intercept form of the equation [tex]\(3x + 2y = 5\)[/tex].
The slope-intercept form of a linear equation is given by [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
1. Start with the given equation:
[tex]\[3x + 2y = 5\][/tex]
2. We need to isolate [tex]\(y\)[/tex]. First, subtract [tex]\(3x\)[/tex] from both sides to move the [tex]\(x\)[/tex]-term to the right side of the equation:
[tex]\[2y = -3x + 5\][/tex]
3. Next, divide every term by [tex]\(2\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[y = \frac{-3x}{2} + \frac{5}{2}\][/tex]
4. Simplify the equation to get it into the standard slope-intercept form:
[tex]\[y = -\frac{3}{2}x + \frac{5}{2}\][/tex]
So the slope-intercept form of the equation [tex]\(3x + 2y = 5\)[/tex] is:
[tex]\[ y = -\frac{3}{2}x + \frac{5}{2} \][/tex]
Now let's compare this to the given options:
1. [tex]\(y = \frac{3}{2}x - \frac{5}{2}\)[/tex]
2. [tex]\(y = \frac{3}{2}x + \frac{5}{2}\)[/tex]
3. [tex]\(y = \frac{2}{3}x + \frac{5}{3}\)[/tex]
4. [tex]\(y = \frac{2}{3}x - \frac{5}{3}\)[/tex]
None of the provided options directly match [tex]\(y = -\frac{3}{2}x + \frac{5}{2}\)[/tex].
Hence, based on the information provided, it appears there may be an issue with the provided options. None of them correctly represent the slope-intercept form of the equation [tex]\(3x + 2y = 5\)[/tex].
The correct slope-intercept form should be [tex]\(y = -\frac{3}{2}x + \frac{5}{2}\)[/tex].
