Question

Stella graphs the equation y=13x – 2
.



Select all statements about Stella's graph that are true.



Responses

The graph is a straight line.
The graph is a straight line.

The line passes through the origin.
The line passes through the origin.

The line passes through the point (0, −2)
.
The line passes through the point begin ordered pair 0 comma negative 2 end ordered pair .

The y-intercept of the line is 2.
The y -intercept of the line is 2.

The slope of the line is 3.

Answer 1

Let's analyze the equation \( y = 13x - 2 \) and determine which statements are true:

1. **The graph is a straight line.**
- **True.** Since it's a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the graph will indeed be a straight line.

2. **The line passes through the origin.**
- **False.** The line does not pass through the origin because when \( x = 0 \), \( y = -2 \), which means it does not go through the point (0, 0).

3. **The line passes through the point (0, −2).**
- **True.** When we substitute \( x = 0 \), we get \( y = 13(0) - 2 = -2 \). Therefore, it does pass through the point (0, -2).

4. **The y-intercept of the line is 2.**
- **False.** The y-intercept \( b \) is -2 (from the equation \( y = 13x - 2 \)), not 2.

5. **The slope of the line is 3.**
- **False.** The slope \( m \) of the line is 13 (from the equation \( y = 13x - 2 \)), not 3.

Therefore, the true statements about Stella's graph are:

- The graph is a straight line.
- The line passes through the point (0, −2).