Why study mathematics? linear equations and the form of point-slope

As we saw in the article "Why Study Mathematics - linear equations and slope-shape, linear equations or functions, only some of the most fundamental areas of mathematics and basic algebra studied. Here we will look to consider and another common way to write linear equations: the point-slope form.

As the name suggests, the shape point-slope equation of a line depends on two things: the slope and a point on the line. Once we know the two things we canWrite the equation of the line. y1 = m - Mathematically, the shape of the point-slope equation of the line passing through the point (x1, y1) with a slope of m, y (x - x1). (The 1 in x and y is actually an index that distinguishes us from X1 and Y1 of Y allows X)

To show how this form is used, take a look at the following example: Suppose you have a line, the track 3, and the point (1, 2). We can easily graph this line byThe point (1, 2) and then use the 3-3 slope unit and then go right one unit. To write the equation of the line, using a smart device. There are variables x and y as a point (x, y). In point-slope form y - y1 = m (x - x1), we have (1, 2) as the point (x1, y1). We then write y - 2 = 3 (x - 1). Using the distributive property on the right side of the equation, we can write y - 2 = 3x - 3 -2 By right, we can write
y = 3x -1. If you have not already guessed, is to make this last equation in slope-intercept.

To see how this form of equation of a line in a real world "is used, take the following example, the information taken from an article in a newspaper. It turns out that the temperature influences the speed. In fact, the optimum temperature for operation below 60 degrees Fahrenheit. If a person was at his best, at 17.6 meters per second, he or sheslow down to about 0.3 meters per second for every 5 degree increase in temperature above 60 degrees. We can use this information to write the linear model of this situation, and then calculate, for example, the optimal speed of 80 degrees.

Let T is the temperature in degrees Fahrenheit. Let P represent the optimal speed in meters per second. The information in this article we know that the optimal speed of 60 degrees 17.6 meters per second. This point(60, 17.6). We use other information to determine the slope of the line for this model. The slope m is equal to the speed variation of the temperature change or M = P / T change We are told that the pace slowed from 0.3 meters per second for every increase of 5 degrees above the 60 ° A decrease is represented by a negative. Using this information we can calculate the slope to -0.3 / 5 or -0.06.

Now that we have a point and the slope, we can write the modelrepresents this situation. We have P - P 1 = m (T - T1) or P - 17.6 = -0.06 (T - 60). Using the distributive property can use this equation in slope-intercept. We get P =- 0.06T + 21.2. To find the optimal speed of 80 degrees, we need to get a compensation of only 80 for the Model T on 16.4.

Situations like these show that math is really used to solve problems that arise in the world. If we're talking about the optimum speed and maximum profit is the key to the mathematicalUnlock our potential for understanding the world around us. And if we understand, we are the power. There was a nice way!