Final answer:
To graph the equation 4x-3y=12, first convert it into the slope-intercept form y=mx+b. The slope is 4/3 and the y-intercept is -4. Plot the y-intercept on the y-axis and move up 4 units and 3 units to the right for the next point, then draw a line through the points.
Step-by-step explanation:
To graph the linear equation 4x-3y=12 using the slope and y-intercept, we first need to convert it into the slope-intercept form which is y=mx+b where m represents the slope and b is the y-intercept.
Here's how to do it:
1. Subtract 4x from both sides of the equation. This gives us: -3y = -4x + 12.
2. Dividing the whole equation by -3 so that y is alone on the left side. This yields: y = 4/3x - 4.
In this equation, the slope (m) is 4/3 and the y-intercept (b) is -4. So, you can start by plotting the y-intercept at -4 on the y-axis. Then, from the y-intercept, you move up 4 units (the slope's numerator) and right 3 units (the slope's denominator) to plot the next point. Draw a line through the points to complete the graph.
Learn more about Graphing Linear Equations