Question

If in 3 days the water level 34 feet and in 10 days 62 feet but before it was 22 what is the equation in standard form

Answer 1

To find the equation in standard form for the water level given your data, we first need to interpret the information provided.

1. Let \( y \) be the water level (in feet).
2. Let \( x \) be the number of days.

From the information given:
- After 3 days, the water level is 34 feet: \( (3, 34) \)
- After 10 days, the water level is 62 feet: \( (10, 62) \)

Since the water level increases with time, we can assume a linear relationship which can be expressed in the form:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

**Step 1: Find the slope (m)**

The slope \( m \) can be calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{62 - 34}{10 - 3} = \frac{28}{7} = 4
\]

So, the slope is 4.

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

We can use one of the points to solve for \( b \). Let's use the point \( (3, 34) \):

\[
y = mx + b
\]
\[
34 = 4(3) + b
\]
\[
34 = 12 + b
\]
\[
b = 34 - 12 = 22
\]

Now we have the equation of the line in slope-intercept form:

\[
y = 4x + 22
\]

**Step 3: Convert to standard form**

The standard form of a linear equation is expressed as:

\[
Ax + By = C
\]

We need to rearrange \( y = 4x + 22 \) into standard form.

1. Subtract \( 4x \) from both sides:
\[
-4x + y = 22
\]

2. Multiply the entire equation by -1 to make the x coefficient positive:
\[
4x - y = -22
\]

Thus, the equation in standard form is:

\[
4x - y = -22
\]