MA005 Calculus 1 Coaching Session 1.2.1 # 15

ma005

#1

Hi this is Swapnila! I am a Student Success Coach and will be explaining some practice problems from the MA005 Calculus course. Today we will review an assigned problem from Unit 1. In the “Homework Assessment” you were asked to solve this problem:

Sketch each line which has slope = m and which goes through the point P. Find the equation of each line.
a) m = 3, P = (2,5) b) m = –2, P = (3,2) c) m = –1/2, P = (1, 4)

Approach all parts of this problem as follows:

  1. Use the given slope and one point to find the other point. Then sketch the line, which passes through these two points.
  2. Use the point slope form of the line to get the equation of the line.

a)
Step 1: Use the given slope and one point to find the other point. Then sketch the line, which passes through these two points.
Given slope m = 3 and point P = (2, 5)
image
That is, change in y values is 3, and change in x values is 1.
Therefore, another point on the line is (2 + 1,5 + 3)=(3, 8)
Plot these two points, and then sketch the line passing through these two points.
It is as below:
image

Step 2: Use the point slope form of the line to get the equation of the line.
Given slope m = 3 and point image
Point slope form is image
Using the given information,
y - 5 = 3(x - 2)
Distributing over the parenthesis,
y - 5 = 3x - 6
Simplifying,
y = 3x - 6 + 5
Simplifying,
y = 3x - 1

Conclusion:
The equation of the line is y = 3x - 1.

b)
Step 1: Use the given slope and one point to find the other point. Then sketch the line, which passes through these two points.
Given slope m = -2 and point P = (3, 2)
image
That is, change in y values is -2, and change in x values is 1.
Therefore, another point from the line is (3 + 1,2 + (-2)) = (4, 0).
Plot these two points, and then sketch the line. It is as below:
image

Step 2: Use the point slope form of the line to get the equation of the line.
Given slope m = -2 and point image
Point slope form is image
Using the given information,
y - 2 = -2(x - 3)
Distributing over the parenthesis,
y - 2 = -2x + 6
Simplifying,
y = -2x + 6 + 2
Simplifying,
y = -2x + 8

Conclusion:
The equation of the line is y = -2x + 8.

c)
Step 1: Use the given slope and one point to find the other point. Then sketch the line, which passes through these two points.
Given slope image and point P = (1, 4)
image

That is, change in y values is -1, and change in x values is 2.
Therefore, another point from the line is (1 + 2, 4 + (-1)) = (3, 3).
Plot these two points, and then sketch the line. It is as below:
image

Step 2: Use the point slope form of the line to get the equation of the line.
Given slope image and point image
Point slope form is image
Using the given information,
image
Distributing over the parenthesis,
image
Simplifying,
image
Simplifying,
image

Conclusion:
The equation of the line is image

In addition to this, I am also attaching the pdf document of the practice problem for your ready reference.
Question 15.pdf (293.2 KB)

Please let me know if you have any question on this problem, or on this topic generally. I will be here in the forum for the next hour.