Mathematical+Reflections+p.+25

 toc



MR1
1. In Problem 1.2, you drew a straight line to model the trend in the (thickness, breaking weight) data. For data that can be modeled with a straight line, how do the y values change as the x calues increase or decrease?

In the graph that I drew in 1.2, it showed that as the y values increase by 1, the x values increase by about 10.  2. Write the general form of the equation for a linear relationship. Explain what each part of the equation means.

A general form of equation for linear relationship is y=mx+b. "m" is the slope in the equation and rate of change in the table. It means as y values increase by 1, x values would increase by "m". "b" is y-intercept in the equation. It is one of the coordinates in the graph which is on the y-axis.  3. If you know the coordinates of two points on a line, how can you find an equation for the line? Use an example if it helps you to explain your thinking.

I could figure out the equation, If I know two coordinates of the graph. First figure out the slope of the equation.(/) After that substitute one of the coordinate in the equation and find the b which is also y-intercept. EX: (1,4) (2,8) y = mx+b m 4-8/1-2 4/1 = 4 y = 4x+b 8 = 4(2)+b 0 = b So the equation will be y=4x.

4. A. Describe the graph of a line that has a negative slope

A graph that has negative slope would look like, a shape of going down. A negative slope would pass 2 and 4 quadrant, and passing other quadrant which would depend on what y-intercept is.  B. What part of the linear equation y=mx+b tells you whether the graph has a negative slope?

The slope "m" tells you whether the graph is negative or positive. If the "m" is negative number the graph would be negative.  C. For a line with a negative slope, how do the y values change as the x values increase?

For a line with a negative slope, as y value increases by 1, x value would increases by m.  5. A. Explain how you would check whether the point (2,7.5) is on the line with equation y=3x+0.5.

I would check that whether (2,7.5) is in y=3x+0.5 by substituting the coordinate (2,7.5) in the equation y=3x+0.5. y=3x +0.5 7.5=3(2)+0.5 7.5=6+0.5 7.5=6.5 Like this, and for this situation it became "7.5=6.5" which means the coordinate (2,7.5)is not one the line with equation y=3x+0.5. <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify"> B. After you substitute a number for x in the equation y=10x+2.8, in what order should you do the calculations to find the value of y? What does the result of your calculations tell you? <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">In order to find value of y, substitute value of x in equation and calculate that side. Then you will be able to figure out the value of y. <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">For example if the x value is 3 and the equation is y=10x+2.8, the y value would be 32.8. <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">y= 10x+2.8 <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">y= 10(3)+2.8 <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">y= 30+2.8 <span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">y= 32.8

<span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">SUMMARY
<span style="FONT-SIZE: 11pt; COLOR: #000000; LINE-HEIGHT: 23px; FONT-FAMILY: '굴림'; LETTER-SPACING: 0px; TEXT-ALIGN: justify">In this investigation, we reviewed many things from last year's such as equation, graph and table. One thing that we learned something new is a concept of "graph model".