Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y?
Draw a dashed line to represent the graph of 5x + 10y = 2000, and shade the portion above the line for positive values of x and y.
Draw a dashed line to represent the graph of 10x + 5y = 2000, and shade the portion above the line for positive values of x and y.
Draw a dashed line to represent the graph of 5x + 10y = 2000, and shade the portion below the line for positive values of x and y.
Draw a dashed line to represent the graph of 10x − 5y = 2000, and shade the portion below the line for positive values of x and y.
Your clue is that it says "LESS than $20"
With that clue... which do you think it is?
To graph the solution to the inequality, we need to first rewrite the inequality in slope-intercept form, which is y = mx + b. The inequality given is 5x + 10y < 2000.
To rewrite it in slope-intercept form, we isolate y by subtracting 5x from both sides:
10y < -5x + 2000
Next, we divide both sides of the equation by 10 to solve for y:
y < (-1/2)x + 200
Now that we have the inequality in slope-intercept form, we can graph it on the coordinate plane. The coefficient of x, which is -1/2, represents the slope of the line, and 200 is the y-intercept.
To graph the inequality, we draw a dashed line with a slope of -1/2 and a y-intercept of 200. Since y is less than the expression (-1/2)x + 200, we shade the portion below the line for positive values of x and y.
Therefore, the correct answer is: Draw a dashed line to represent the graph of 5x + 10y = 2000, and shade the portion below the line for positive values of x and y.