## The Slope Of A Fairly Flat Upward-sloping Line Will Be A

One question we might want to ask about Emma is how much her purchasing habits respond to price. Look at the demand curve pictured in Figure 2A-5. If this curve is very steep, Emma purchases nearly the same number of novels regardless Figure 2A-5

Calculating the Slope of a Line. To calculate the slope of the demand curve, we can look at the changes in the x- and y-coordinates as we move from the point (21 novels, \$6) to the point (13 novels, \$8). The slope of the line is the ratio of the change in the y-coordinate (—2) to the change in the x-coordinate (+8), which equals —1/4.

of Novels Purchased of Novels Purchased

### Figure 2A-5

Calculating the Slope of a Line. To calculate the slope of the demand curve, we can look at the changes in the x- and y-coordinates as we move from the point (21 novels, \$6) to the point (13 novels, \$8). The slope of the line is the ratio of the change in the y-coordinate (—2) to the change in the x-coordinate (+8), which equals —1/4.

of whether they are cheap or expensive. If this curve is much flatter, Emma purchases many fewer novels when the price rises. To answer questions about how much one variable responds to changes in another variable, we can use the concept of slope.

The slope of a line is the ratio of the vertical distance covered to the horizontal distance covered as we move along the line. This definition is usually written out in mathematical symbols as follows:

Ay slope = —, F Ax where the Greek letter A (delta) stands for the change in a variable. In other words, the slope of a line is equal to the "rise" (change in y) divided by the "run" (change in x). The slope will be a small positive number for a fairly flat upward-sloping line, a large positive number for a steep upward-sloping line, and a negative number for a downward-sloping line. A horizontal line has a slope of zero because in this case the y-variable never changes; a vertical line is defined to have an infinite slope because the y-variable can take any value without the x-variable changing at all.

What is the slope of Emma's demand curve for novels? First of all, because the curve slopes down, we know the slope will be negative. To calculate a numerical value for the slope, we must choose two points on the line. With Emma's income at \$30,000, she will purchase 21 novels at a price of \$6 or 13 novels at a price of \$8. When we apply the slope formula, we are concerned with the change between these two points; in other words, we are concerned with the difference between them, which lets us know that we will have to subtract one set of values from the other, as follows:

Ay first y-coordinate - second y-coordinate 6-8 -2 -1 sope Ax first x-coordinate—second x-coordinate 21-13 8 4

Figure 2A-5 shows graphically how this calculation works. Try computing the slope of Emma's demand curve using two different points. You should get exactly the same result, -1/4. One of the properties of a straight line is that it has the same slope everywhere. This is not true of other types of curves, which are steeper in some places than in others.

The slope of Emma's demand curve tells us something about how responsive her purchases are to changes in the price. A small slope (a number close to zero) means that Emma's demand curve is relatively flat; in this case, she adjusts the number of novels she buys substantially in response to a price change. A larger slope (a number farther from zero) means that Emma's demand curve is relatively steep; in this case, she adjusts the number of novels she buys only slightly in response to a price change.