To convert the given equations to the slope-intercept form [tex]\( y = mx + b \)[/tex], we need to solve each equation for [tex]\( y \)[/tex].
### Equation a: [tex]\(-3x + 2y = 4\)[/tex]
1. Start with the given equation:
[tex]\[
-3x + 2y = 4
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex]. Add [tex]\( 3x \)[/tex] to both sides of the equation to get:
[tex]\[
2y = 3x + 4
\][/tex]
3. Divide every term by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{3}{2}x + 2
\][/tex]
Thus, the slope-intercept form of the first equation is:
[tex]\[
y = \frac{3}{2}x + 2
\][/tex]
Here, the slope [tex]\( m = \frac{3}{2} \)[/tex] and the y-intercept [tex]\( b = 2 \)[/tex].
### Equation b: [tex]\(-x - 2y = 5\)[/tex]
1. Start with the given equation:
[tex]\[
-x - 2y = 5
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex]. Add [tex]\( x \)[/tex] to both sides of the equation to get:
[tex]\[
-2y = x - 5
\][/tex]
3. Divide every term by [tex]\(-2\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = -\frac{1}{2}x - \frac{5}{2}
\][/tex]
Thus, the slope-intercept form of the second equation is:
[tex]\[
y = -\frac{1}{2}x - \frac{5}{2}
\][/tex]
Here, the slope [tex]\( m = -\frac{1}{2} \)[/tex] and the y-intercept [tex]\( b = -\frac{5}{2} \)[/tex].
### Summary
- For equation [tex]\(-3x + 2y = 4\)[/tex], the slope-intercept form is [tex]\( y = \frac{3}{2}x + 2 \)[/tex].
- For equation [tex]\(-x - 2y = 5\)[/tex], the slope-intercept form is [tex]\( y = -\frac{1}{2}x - \frac{5}{2} \)[/tex].
These are the required slope-intercept forms for the given equations.
