You are tasked to graphing the equation

Question

𝑦
=
7
𝑥

+

5
y=7x + 5 Click Here for Help Video

Our initial point (the y-intercept) is the point is (
,
)

To plot a 2nd point we would start at our initial point and go up
7
7 and right
1
1 and this is the point (
,
)

55

Answer 1

To graph the equation \( y = 7x + 5 \), we can follow these steps:

1. Find the y-intercept: The y-intercept is the point where the line crosses the y-axis. This occurs when \( x = 0 \). \[ y = 7(0) + 5 = 5 \] So the y-intercept is the point \( (0, 5) \).

2. Plot the first point: The first point based on the y-intercept is \( (0, 5) \).

3. Use the slope to find the second point: The slope of the line is \( 7 \), which means for every 1 unit we move to the right (positive x direction), we move up \( 7 \) units (positive y direction).

   Starting from the y-intercept \( (0, 5) \):

   • Move right 1 unit to \( x = 1 \)
   • Move up \( 7 \) units from \( y = 5 \) to \( y = 5 + 7 = 12 \)

   This gives us the second point \( (1, 12) \).

4. Summary of points:

   • The first point (y-intercept): \( (0, 5) \)
   • The second point: \( (1, 12) \)

You can now plot these points on a graph and draw a line through them to represent the equation \( y = 7x + 5 \).