Question

One point negative one, 10 another 0.1, 3.6 what equation is shown in the graph y =

Answer 1

To find the equation of a line that passes through the given points, we need to identify the two points provided:

1. Point A: (-1, 10)
2. Point B: (0.1, 3.6)

We can use the slope-intercept form of the equation of a line, which is:

\[ y = mx + b \]

Where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.

### Step 1: Calculate the slope (m)

The slope \( m \) between two points is given by the formula:

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

Substituting the points (where \( (x_1, y_1) = (-1, 10) \) and \( (x_2, y_2) = (0.1, 3.6) \)):

\[
m = \frac{3.6 - 10}{0.1 - (-1)} = \frac{-6.4}{1.1} \approx -5.818
\]

### Step 2: Find the y-intercept (b)

We can use one of the points to solve for \( b \). Let's use point B (0.1, 3.6):

\[
3.6 = -5.818(0.1) + b
\]

Calculating the right side:

\[
3.6 = -0.5818 + b
\]
\[
b = 3.6 + 0.5818 = 4.1818
\]

### Step 3: Write the final equation

Now we have \( m \) and \( b \):

\[
y = -5.818x + 4.1818
\]

So the equation of the line is:

\[
y \approx -5.818x + 4.182
\]

You can round the coefficients or leave them as is based on your preference for significant figures.