To graph the equation \( y = 4x + 1 \), we'll identify the slope and y-intercept and then plot the points according to that information.
-
Identify the y-intercept: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation \( y = 4x + 1 \), when \( x = 0 \):
\[ y = 4(0) + 1 = 1 \]
So, the y-intercept is at the point (0, 1).
-
Identify the slope: The slope is the coefficient of \( x \), which is 4. This means that for every 1 unit you move to the right (increase in \( x \)), you move up 4 units (increase in \( y \)).
-
Plot the points: Starting from the y-intercept (0, 1), you can plot additional points using the slope.
-
From (0, 1), move 1 unit to the right to \( x = 1 \), then move up 4 units:
- New point: \( (1, 5) \)
-
You can also go in the opposite direction. From (0, 1), move 1 unit to the left to \( x = -1 \), then move down 4 units:
- New point: \( (-1, -3) \)
Now you have a few points to plot: (0, 1), (1, 5), and (-1, -3).
-
-
Draw the line: Connect these points with a straight line, and you have the graph of the equation \( y = 4x + 1 \).
If you have graphing tools, you can plot these points accordingly.