Question

What is the y-intercept of this line

(Line goes from (0, -3) (3, 0))

What is the equation of the libe

Answer 1

To find the equation of the line that passes through the points (0, -3) and (3, 0), we can use the slope-intercept form of the equation of a line, which is given by:

\[
y = mx + b
\]

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

### 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:

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

Using the points (0, -3) \((x_1, y_1)\) and (3, 0) \((x_2, y_2)\):

\[
m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1
\]

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

The y-intercept \( b \) is the y-coordinate of the point where the line crosses the y-axis, which is the \( y \)-coordinate when \( x = 0 \). From the point (0, -3), we can see that:

\[
b = -3
\]

### Step 3: Write the equation of the line

Now that we have the slope and y-intercept, we can write the equation of the line:

\[
y = 1x - 3 \quad \text{or simply} \quad y = x - 3
\]

### Summary

- The y-intercept of the line is \( -3 \).
- The equation of the line is \( y = x - 3 \).