Question

Put into slope intercept form
5x-2y=14
10x-2y=-6
8x+6y=12
6x-10y=20
3x+9y= -36

Answer 1

To convert each given equation into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we will solve for \( y \).

1. **Equation: \( 5x - 2y = 14 \)**
\[
-2y = -5x + 14 \quad \text{(Subtract 5x from both sides)}
\]
\[
y = \frac{5}{2}x - 7 \quad \text{(Divide by -2)}
\]

2. **Equation: \( 10x - 2y = -6 \)**
\[
-2y = -10x - 6 \quad \text{(Subtract 10x from both sides)}
\]
\[
y = 5x + 3 \quad \text{(Divide by -2)}
\]

3. **Equation: \( 8x + 6y = 12 \)**
\[
6y = -8x + 12 \quad \text{(Subtract 8x from both sides)}
\]
\[
y = -\frac{4}{3}x + 2 \quad \text{(Divide by 6)}
\]

4. **Equation: \( 6x - 10y = 20 \)**
\[
-10y = -6x + 20 \quad \text{(Subtract 6x from both sides)}
\]
\[
y = \frac{3}{5}x - 2 \quad \text{(Divide by -10)}
\]

5. **Equation: \( 3x + 9y = -36 \)**
\[
9y = -3x - 36 \quad \text{(Subtract 3x from both sides)}
\]
\[
y = -\frac{1}{3}x - 4 \quad \text{(Divide by 9)}
\]

Now, we have all the equations in slope-intercept form:

1. \( y = \frac{5}{2}x - 7 \)
2. \( y = 5x + 3 \)
3. \( y = -\frac{4}{3}x + 2 \)
4. \( y = \frac{3}{5}x - 2 \)
5. \( y = -\frac{1}{3}x - 4 \)