Question

or
Graph this line using the slope and y-intercept:
y=7x+2

Answer 1

To graph the line given by the equation \( y = 7x + 2 \), we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where:

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

From the equation \( y = 7x + 2 \):

- The slope \( m \) is 7.
- The y-intercept \( b \) is 2.

### Steps to graph the line:

1. **Plot the y-intercept**: Start by plotting the y-intercept on the graph. Since \( b = 2 \), you will place a point at (0, 2) on the y-axis.

2. **Use the slope to find another point**: The slope of 7 can be expressed as \( \frac{7}{1} \). This means that for every 7 units you move up in the y-direction, you move 1 unit to the right in the x-direction.

- Starting from the y-intercept (0, 2):
- Move 1 unit to the right (to \( x = 1 \)).
- Move up 7 units (from \( y = 2 \) to \( y = 9 \)).
- This gives you the point (1, 9).

3. **Draw the line**: Connect the two points (0, 2) and (1, 9) with a straight line. Extend the line in both directions, and use arrows to indicate that it continues indefinitely.

### Summary of points to plot:
- (0, 2) (y-intercept)
- (1, 9) (using the slope)

### Final result:
You should have a straight line that passes through the points (0, 2) and (1, 9) with a steep upward slope.