Question

Give the slope and the​ y-intercept of the line with the given equation. ​ Then, graph the linear equation.
y equals 3 x plus 7
Question content area bottom left
Part 1
What is the​ slope? Select the correct choice below and fill in any answer boxes within your choice.
A.
The slope is
  
enter your response here.
​(Simplify your​ answer.)
B.
The slope is undefined.
Part 2
What is the​ y-intercept? Select the correct choice below and fill in any answer boxes within your choice.
A.
The​ y-intercept is
  
enter your response here.
​(Type an integer or a simplified​ fraction.)
B.
There is no​ y-intercept.
Part 3
Graph the equation.

Answer 1

To analyze the equation \(y = 3x + 7\), we can identify the slope and y-intercept from the standard form of a linear equation, which is in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Part 1: Slope
The given equation is \(y = 3x + 7\).
- The slope \(m\) is the coefficient of \(x\).
- Here, the slope is **3**.

**Correct Choice for Slope:**
A. The slope is **3**.

### Part 2: Y-intercept
The y-intercept \(b\) is the constant term in the equation when \(x = 0\).
- In this case, the y-intercept is **7**.

**Correct Choice for Y-intercept:**
A. The y-intercept is **7**.

### Part 3: Graph the Equation
To graph the equation \(y = 3x + 7\):
1. Start by plotting the y-intercept (0, 7) on the graph.
2. From this point, use the slope to find another point. The slope of 3 means that for every increase of 1 in \(x\), \(y\) increases by 3.
- From (0, 7): If \(x = 1\), then \(y = 3(1) + 7 = 10\). Plot the point (1, 10).

3. Draw a line through the points (0, 7) and (1, 10). This line represents the equation \(y = 3x + 7\).

### Recap
- **Slope:** 3
- **Y-intercept:** 7
- **Graph:** A line that crosses the y-axis at (0, 7) and rises steeply due to the slope of 3.

Would you like any further assistance with this topic?