How do you plot y = 3x - 4 on a graph?

To plot \( y = 3x - 4 \), find points by substituting values for \( x \) and then draw the line through them.

First, understand that \( y = 3x - 4 \) is a linear equation in the form \( y = mx + c \), where \( m \) is the gradient (slope) and \( c \) is the y-intercept. Here, the gradient \( m \) is 3, meaning the line rises 3 units for every 1 unit it moves to the right. The y-intercept \( c \) is -4, which is where the line crosses the y-axis.

To plot the graph, start by finding the y-intercept. Set \( x = 0 \) in the equation:
\[ y = 3(0) - 4 = -4 \]
So, the point (0, -4) is on the graph. Plot this point on the y-axis.

Next, choose another value for \( x \) to find a second point. For example, let \( x = 1 \):
\[ y = 3(1) - 4 = 3 - 4 = -1 \]
So, the point (1, -1) is also on the graph. Plot this point.

For a third point, let \( x = 2 \):
\[ y = 3(2) - 4 = 6 - 4 = 2 \]
So, the point (2, 2) is on the graph. Plot this point as well.

Now, draw a straight line through these points. This line represents the equation \( y = 3x - 4 \). Ensure your line extends across the graph, showing the linear relationship between \( x \) and \( y \). By plotting these points and drawing the line, you have successfully graphed the equation.