Final answer:
To correctly graph the equation 4x - 3y = -1, first convert it to slope-intercept form to identify the slope (4/3) and y-intercept (1/3), then plot the y-intercept and use the slope to find a second point. Connect these points with a straight line to represent the graph of the equation.
Step-by-step explanation:
To graph the equation 4x - 3y = -1, you need to first solve for y to get it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. By rearranging the equation, we get 3y = 4x + 1, and then dividing both sides by 3 gives us y = (4/3)x + 1/3. The slope here is (4/3) and the y-intercept is (1/3), which means the line will cross the y-axis at (0, 1/3).
To graph this, you start plotting at the point (0, 1/3) on the y-axis, then use the slope to find another point. Since the slope is 4/3, you would rise 4 units and run 3 units to the right from the y-intercept to find a second point. Plot this second point, then draw a straight line through both points to represent the equation.