What graph illustrates the inequality 4 x + 3 y

Question

What graph illustrates the inequality 4 x + 3 y < 5?

Quizplus · Accepted Answer

The inequality 4x + 3y < 5 can be rewritten as y < (-4/3)x + (5/3), which is the equation of a line with a slope of -4/3 and a y-intercept of 5/3. To graph this, you can plot the y-intercept at (0,5/3) and then use the slope to find at least one other point. Since the slope is negative, you can move down 4 units and to the right 3 units to get to another point on the line. Plot that point at (3,1), and then draw a dotted line connecting the two points.

The inequality is y < (-4/3)x + (5/3), so you want to shade below the line to represent all of the points that satisfy the inequality. This is the shaded region labeled as "Option C" in the multiple choice options.

What Graph Illustrates the Inequality 4 X + 3 Y