Hello Math 25 class. I am Henry Walsh and I have loved math since my Algebra 1 class. I love how I can use it in my daily life for reasons that I would never think about. Math is something I love to do and Math 25 is a way for me to do it.
Finding slopes is essential to an individuals math career. The slope of a line is the measure of the "steepness" of that line. It is usually represented by the variable m. Here is a video to show anq in depth description on how to find slopes.
19.4.
The slope of a line is a measure of how steep the line is. It is calculated by dividing the change in y-coordinates by the corresponding change in x-coordinates between the two points on the line: slope= change in y/change in x. Calculate the slope of the line that goes through the two points ( 1, 3 ) and ( 7, 6 ). Calculate the slope of the line that goes through the two points ( 0, 0 ) and ( 9, 6 ). Which line is steeper?
The slope of a line is a measure of how steep the line is. It is calculated by dividing the change in y-coordinates by the corresponding change in x-coordinates between the two points on the line: slope= change in y/change in x. Calculate the slope of the line that goes through the two points ( 1, 3 ) and ( 7, 6 ). Calculate the slope of the line that goes through the two points ( 0, 0 ) and ( 9, 6 ). Which line is steeper?
To solve this question you need to take your coordinates and plug them into the slope equation. So the math and you will get the answer. Then you need to put it in slope intercept form y=mx+b. With the y-intercept or b being 0 the answer would just be in the y=mx form. I like this problem because it includes finding slopes but it also includes comparing slopes.
20.8.
Draw the segment from ( 3, 1 ) to ( 5, 6 ), and the segment form ( 0, 5 ) to ( 0, 2 ). Calculate their slopes. You should notice that the segments are equally steep, and yet they differ in a significant way. Do your slope calculations reflect this difference?
Draw the segment from ( 3, 1 ) to ( 5, 6 ), and the segment form ( 0, 5 ) to ( 0, 2 ). Calculate their slopes. You should notice that the segments are equally steep, and yet they differ in a significant way. Do your slope calculations reflect this difference?
You solve this question in your standard way by putting the coordinates in the slope equation. But this question brings up negative sloped in one of the answers. Negative slopes are the same steepness as the positive answer but they make lines that go the opposite way on the graph. I like this question for that reason of introducing negative slopes.
22.4.
A Car and a small truck started out from Exeter at 8:00 am. Their distances form Exeter, recorded at hourly intervals are recorded in the tables at right. Plot this information on the same set of axes and draw two lines connecting the points in each set of data. What is the slop of each line? What is the meaning of these slopes in the context of this problem?
A Car and a small truck started out from Exeter at 8:00 am. Their distances form Exeter, recorded at hourly intervals are recorded in the tables at right. Plot this information on the same set of axes and draw two lines connecting the points in each set of data. What is the slop of each line? What is the meaning of these slopes in the context of this problem?
To find the slope you need to just do the standard thing. Then to put them in your graph you need to take the data from your table and put them on a graph. I like this problem because it includes finding slopes but it also includes comparing slopes.
22.5
(Continuation) Let t be the number of hours each vehicle has been traveling since 8:00 am (thus t=0 means 8:00 am), and let d be the number of miles traveled after t hours. For each vehicle, write and equation relating d and t.
(Continuation) Let t be the number of hours each vehicle has been traveling since 8:00 am (thus t=0 means 8:00 am), and let d be the number of miles traveled after t hours. For each vehicle, write and equation relating d and t.
TO solve your sweater you need use your slope answers in the slope intercept equation form. Again the y-intercept is 0 so you just put it in y=mx form. I like this problem because it makes you use the slope in the point slope form. Something that is essential in learning how to use slopes.
26.3
Write and equation in point-slope form for
a. the line that goes through ( 2, 5 ) and ( 6, -3 );
b. the line that goes through point ( h, k ) and that has a slope m
Write and equation in point-slope form for
a. the line that goes through ( 2, 5 ) and ( 6, -3 );
b. the line that goes through point ( h, k ) and that has a slope m
Solving the first part of this equation is simple. Just put the coordinates in the equation. The second part tests your understanding of the slope and coordinates. k is the y-intercept and your slope is m so you insert those into your slope intercept form. I like this problem because it tests your knowledge of the slope intercept equation form.
In the end slopes seem challenging from the outside but in actuality it is very simple once you get past that first wave of difficulty they become very easy. They are essential to your math education as well especially in more advanced classes. I chose these problems because they let you get the handle of the slope equation and then you have to start using variables instead. In the end you have to know how to include your slope in the point slope form.