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Understanding the slope-intercept form is crucial for graphing linear equations. The slope-intercept form of a line is given by the equation \( y = mx + b \). Here, \( 'm' \) represents the slope of the line and \( 'b' \) represents the y-intercept, which is where the line crosses the y-axis.

In the exercise, the equation \( 3y - 4x = 0 \) is first rewritten into the slope-intercept form as \( y = \frac{4}{3}x \). This equation shows that the slope \( m \) is \( \frac{4}{3} \) and the y-intercept \( b \) is 0.

The slope tells us that for every 3 units we move horizontally (to the right), we move 4 units vertically (upwards). This slope provides the angle or the steepness of the line.

The domain and range of a function help describe the possible values that the variables can take.

The domain of a function includes all the possible x-values. For linear equations like \( y = \frac{4}{3}x \), there are no restrictions on the values x can take. This means the domain is all real numbers, which we symbolically write as \( (-\infty, \infty) \).

Similarly, the range includes all the possible y-values that the function can produce. Since the line extends infinitely in both directions, there are also no restrictions on y. Therefore, the range is also all real numbers, \( (-\infty, \infty) \).

Plotting points is a fundamental skill for graphing linear equations. To plot a line given an equation, you start by identifying specific points through which the line passes.

For the equation \( y = \frac{4}{3}x \), the process begins by plotting the y-intercept, which is the point (0,0) in this case.

You then use the slope \( \frac{4}{3} \) to find additional points. From the origin, move 4 units up (adding 4 to y) and 3 units to the right (adding 3 to x). This gives the point (3,4).

Draw a straight line through these points to complete the graph. Plotting these points helps visualize the function and understand how changes in x affect y.