Final answer:
To graph the linear inequality 4x - 3y < -12 over the set of real numbers, solve for y in terms of x, then plot the line with a slope of (4/3) and a y-intercept of 4. Shade the region above the line to represent all the points that satisfy the inequality.
Step-by-step explanation:
To graph the linear inequality 4x - 3y < -12, we first need to solve for y in terms of x:
4x - 3y < -12
-3y < -12 - 4x
y > (4/3)x + 4
The inequality is now in slope-intercept form, y > mx + b, where m is the slope and b is the y-intercept. The slope is (4/3), which means the line will be sloping upward to the right. The y-intercept is 4, which is where the line intersects the y-axis.
To graph the inequality, we draw a dotted line with a slope of (4/3) and a y-intercept of 4. Since the inequality is y > (4/3)x + 4, we shade the region above the line to represent all the points that satisfy the inequality.
Keywords: linear inequality, graph, real numbers, slope-intercept form, slope, y-intercept