Question

1 the graph represents the perimeter, y, in units, for an equilateral triangle with side length of x units. the slope of the line is 3. 2 the amount of money, y, in a cash box after x tickets are purchased for carnival games. the slope of the line is 1/4. 3 the number of chapters read, y, after x days. the slope of the line is 3/4. 4 the graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. the slope of the line is 2

Explanation:

Step1: Find the slope for each situation

• For an equilateral triangle: The formula for the perimeter \(y\) of an equilateral triangle with side - length \(x\) is \(y = 3x\). Using the slope - intercept form \(y=mx + b\) (where \(b = 0\) in this case), the slope \(m = 3\).
• For the money in the cash - box: Let's assume the relationship is \(y=mx + b\). If we take two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. Suppose when \(x = 0\), \(y=b\) (initial amount) and when \(x = 4\), \(y=b + 1\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(m=\frac{1}{4}\).
• For the number of chapters read: Let's assume \(y=\frac{3}{4}x\) (using the slope - intercept form \(y = mx\) since \(b = 0\) if we start counting from day \(x = 0\)). The slope \(m=\frac{3}{4}\).
• For the muffin delivery cost: Let's assume the relationship is \(y = mx\) (assuming no fixed cost for simplicity, or \(b = 0\) if we consider only the cost per muffin). If we take two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. For example, if \(x=1,y = 2\) and \(x = 2,y=4\), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 2}{2 - 1}=2\).

Step2: Match the slope with the graph

• The graph of \(y = 3x\) (perimeter of equilateral triangle) has a steeper slope.
• The graph of \(y=\frac{1}{4}x\) (money in cash - box) has a gentle slope.
• The graph of \(y=\frac{3}{4}x\) (chapters read) has a moderate slope.
• The graph of \(y = 2x\) (muffin cost) has a relatively steep slope.

Answer:

1. C
2. A
3. D
4. B