Sure, let's rewrite each of the given equations in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope of the line and [tex]\( b \)[/tex] represents the y-intercept.
### 1. Equation: [tex]\( 7x + 2y = 14 - 5 \)[/tex]
First, simplify the equation:
[tex]\[ 7x + 2y = 9 \][/tex]
Next, isolate [tex]\( y \)[/tex] by moving [tex]\( 7x \)[/tex] to the right side:
[tex]\[ 2y = -7x + 9 \][/tex]
Divide both sides of the equation by 2:
[tex]\[ y = -\frac{7}{2}x + \frac{9}{2} \][/tex]
Thus, the slope (m) is [tex]\( -\frac{7}{2} \)[/tex] and the y-intercept (b) is [tex]\( \frac{9}{2} \)[/tex].
### 2. Equation: [tex]\( 2y = 14 - 7x \)[/tex]
Rearrange to isolate [tex]\( y \)[/tex]:
[tex]\[ y = -\frac{7}{2}x + 7 \][/tex]
Thus, the slope (m) is [tex]\( -\frac{7}{2} \)[/tex] and the y-intercept (b) is 7.
### 3. Equation: [tex]\( 2y = -7x + 14 \)[/tex]
This equation is already close to the slope-intercept form. We simply rearrange to make it explicit:
[tex]\[ y = -\frac{7}{2}x + 7 \][/tex]
Thus, the slope (m) is [tex]\( -\frac{7}{2} \)[/tex] and the y-intercept (b) is 7.
### 4. Equation: [tex]\( 3x + 6y = -9 \)[/tex]
First, isolate [tex]\( y \)[/tex] by moving [tex]\( 3x \)[/tex] to the right side:
[tex]\[ 6y = -3x - 9 \][/tex]
Divide both sides of the equation by 6:
[tex]\[ y = -\frac{1}{2}x - \frac{-1}{2} \][/tex]
Thus, the slope (m) is [tex]\( -\frac{1}{2} \)[/tex] and the y-intercept (b) is [tex]\( -\frac{3}{2} \)[/tex].
### Summary
1. For the equation [tex]\( 7x + 2y = 14 - 5 \)[/tex]:
- Slope: [tex]\( -\frac{7}{2} \)[/tex]
- Y-intercept: [tex]\( \frac{9}{2} \)[/tex]
2. For the equation [tex]\( 2y = 14 - 7x \)[/tex]:
- Slope: [tex]\( -\frac{7}{2} \)[/tex]
- Y-intercept: 7
3. For the equation [tex]\( 2y = -7x + 14 \)[/tex]:
- Slope: [tex]\( -\frac{7}{2} \)[/tex]
- Y-intercept: 7
4. For the equation [tex]\( 3x + 6y = -9 \)[/tex]:
- Slope: [tex]\( -\frac{1}{2} \)[/tex]
- Y-intercept: [tex]\( -\frac{3}{2} \)[/tex]
