Question

Graph and then find the solution for y= 7/6x+4

Answer 1

To graph the equation \( y = \frac{7}{6}x + 4 \), we can follow these steps:

### Step 1: Identify the y-intercept
The y-intercept is the value of \( y \) when \( x = 0 \).
\[
y = \frac{7}{6}(0) + 4 = 4
\]
So the y-intercept is at the point \( (0, 4) \).

### Step 2: Identify the slope
The slope of the line is \( \frac{7}{6} \). This means that for every \( 6 \) units you move to the right along the x-axis, the line will go up \( 7 \) units.

### Step 3: Plot the points
1. Start by plotting the y-intercept \( (0, 4) \).
2. Using the slope of \( \frac{7}{6} \), from \( (0, 4) \):
- Move \( 6 \) units to the right (to \( x = 6 \)), and then move \( 7 \) units up. This gives us the point \( (6, 11) \).
- Alternatively, you could also move \( -6 \) units to the left (to \( x = -6 \)) and move \( -7 \) units down to find the point \( (-6, -3) \).

### Step 4: Draw the line
Connect the points \( (0, 4) \) and \( (6, 11) \) (or any other points you plotted) with a straight line.

### Step 5: Find a specific solution
To find a solution for a specific value of \( x \):
- For example, if \( x = 6 \):
\[
y = \frac{7}{6}(6) + 4 = 7 + 4 = 11
\]
This gives the point \( (6, 11) \) which is on the line.

You can similarly find \( y \) for other values of \( x \) if needed.

### Summary
The equation \( y = \frac{7}{6}x + 4 \) is a straight line with a slope of \( \frac{7}{6} \) and a y-intercept at \( (0, 4) \). You can graph it using the above steps, and you can find specific solutions by substituting values for \( x \).