For each of the following given below, find th slope and the y-intercept.
`5x=4y+7`

Answer

To find the slope and the y-intercept of the equation \(5x = 4y + 7\), we will follow these steps:

### Step 1: Rearrange the equation into the slope-intercept form
The slope-intercept form of a line is given by the equation \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

Starting with the given equation:
\[ 5x = 4y + 7 \]

### Step 2: Isolate \(y\)
We need to isolate \(y\) on one side of the equation. First, we can move \(7\) to the left side:
\[ 5x - 7 = 4y \]

Next, divide every term by \(4\) to solve for \(y\):
\[ y = \frac{5}{4}x - \frac{7}{4} \]

### Step 3: Identify the slope and y-intercept
Now that we have the equation in the form \(y = mx + c\):
\[ y = \frac{5}{4}x - \frac{7}{4} \]

From this equation:
- The slope \(m\) is \(\frac{5}{4}\).
- The y-intercept \(c\) is \(-\frac{7}{4}\).

### Final Answer
- Slope (m) = \(\frac{5}{4}\)
- Y-intercept (c) = \(-\frac{7}{4}\)

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