Convert the following equations into slope-intercept form and find their slope and `y`-intercepts.
`(i) 5x+12y=26` `(ii) 6x-8y+5=0`

Answer

To convert the given equations into slope-intercept form and find their slope and y-intercepts, we will follow these steps:

### (i) For the equation \( 5x + 12y = 26 \):

**Step 1:** Isolate \( y \) on one side of the equation.
\[ 12y = -5x + 26 \]

**Step 2:** Divide every term by 12 to solve for \( y \).
\[ y = -\frac{5}{12}x + \frac{26}{12} \]

**Step 3:** Simplify \( \frac{26}{12} \).
\[ y = -\frac{5}{12}x + \frac{13}{6} \]

Now, we have the equation in slope-intercept form \( y = mx + c \) where:
- Slope \( m = -\frac{5}{12} \)
- y-intercept \( c = \frac{13}{6} \)

### (ii) For the equation \( 6x - 8y + 5 = 0 \):

**Step 1:** Rearrange the equation to isolate \( y \).
\[ -8y = -6x - 5 \]

**Step 2:** Multiply through by -1 to make \( y \) positive.
\[ 8y = 6x + 5 \]

**Step 3:** Divide every term by 8 to solve for \( y \).
\[ y = \frac{6}{8}x + \frac{5}{8} \]

**Step 4:** Simplify \( \frac{6}{8} \).
\[ y = \frac{3}{4}x + \frac{5}{8} \]

Now, we have the equation in slope-intercept form \( y = mx + c \) where:
- Slope \( m = \frac{3}{4} \)
- y-intercept \( c = \frac{5}{8} \)

### Summary of Results:
1. For \( 5x + 12y = 26 \):
- Slope \( m = -\frac{5}{12} \)
- y-intercept \( c = \frac{13}{6} \)

2. For \( 6x - 8y + 5 = 0 \):
- Slope \( m = \frac{3}{4} \)
- y-intercept \( c = \frac{5}{8} \)