Question

if in 3 days the water us 34 feet and in 10 days it is 62 feet but before it was 22 what is the slope in intercept form

Answer 1

To find the slope in intercept form (which is typically \(y = mx + b\)), we first need to identify the slope and the y-intercept from the information provided.

You gave two points:
- After 3 days, the water level is 34 feet: \( (3, 34) \)
- After 10 days, the water level is 62 feet: \( (10, 62) \)

**Step 1: Calculate the slope \( m \)**

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the values:

\[
m = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4
\]

**Step 2: Use the slope to find the y-intercept \( b \)**

We can use one of the points and the slope to find the y-intercept \( b \). We'll use the point \( (3, 34) \):

Substituting \( x = 3 \), \( y = 34 \), and \( m = 4 \) into the slope-intercept form \( y = mx + b \):

\[
34 = 4(3) + b
\]

Calculating that gives:

\[
34 = 12 + b
\]
\[
b = 34 - 12 = 22
\]

**Step 3: Write the equation in slope-intercept form**

Now that we have both the slope \( m \) and the y-intercept \( b \), we can write the equation:

\[
y = 4x + 22
\]

**Conclusion:**

The slope-intercept form of the equation is:

\[
y = 4x + 22
\]