Question

Fill in the Blank 2 points
What is the y-intercept of this line?
10-
(3, 0)
Vx
-10
10
₽ (0,-3)
-10 ÷
y-intercept =
choose your answer...
What is the equation of the line? choose your answer...

Answer 1

The equation of the line part is wrong it isn’t an option

Answer 2

To find the y-intercept and the equation of the line given points (3, 0) and (0, -3), let’s solve it step by step.

1. **Finding the y-Intercept:**
The y-intercept occurs where the line crosses the y-axis (where x=0). Given the point (0, -3), the y-intercept is:
\[
\text{y-intercept} = -3
\]

2. **Finding the Equation of the Line:**
To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points provided: (3, 0) and (0, -3).

The formula for slope \( m \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting in the coordinates:
- \( (x_1, y_1) = (3, 0) \)
- \( (x_2, y_2) = (0, -3) \)

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

3. **Putting the Equation Together:**
We now have the slope \( m = 1 \) and y-intercept \( b = -3 \), so the equation of the line is:
\[
y = 1x - 3 \quad \text{or simply} \quad y = x - 3
\]

### Answers:
- **y-intercept =** -3
- **Equation of the line =** y = x - 3

Answer 3

I apologize for any confusion. Let's reevaluate the information provided to ensure we arrive at the correct equation of the line based on the coordinates you've provided.

Given the points (3, 0) and (0, -3):

1. **Finding the Slope:**
Using the formula for slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
- Let \( (x_1, y_1) = (3, 0) \)
- Let \( (x_2, y_2) = (0, -3) \)

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

So the slope \( m = 1 \).

2. **Using the Point-Slope Form:**
We can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
Let's use the point (3, 0):
\[
y - 0 = 1(x - 3)
\]
This simplifies to:
\[
y = x - 3
\]

However, if there is a specified format that is different from what I've given (for example, if it needs to be expressed differently), please provide those options, and I can help you derive the correct equation accordingly. If there is a specific form or mention of intercepts that you are looking for, please clarify, and I will correct or adjust my response to meet those options accurately.