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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Slopes & Lines

Grade: 1400-a Lesson: S3-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the equation of the line passing through the points P(4,3) and Q(2,-1).
2	Formula:	We can use the point-slope form of a linear equation	y - y1 = m(x - x1)
3	Formula:	First, let’s find the slope (m) using the two given points	m = \$(y2 - y1) / (x2 - x1)\$m
4	Step	Substitute the values into the slope formula and calculate the m	m = \$(-1 - 3) / (2 - 4)\$ m = \$(-4)/(-2)\$ m = \$2\$
5	Hint	Now that we have the slope (m = 2) and one of the points (P) (x1 = 4, y1 = 3) we can use the point-slope form to write the equation	y - y1 = m(x - x1)
6	Step	Substitute the values and simplify the equation	y - 3 = 2(x - 4) y - 3 = 2x - 8
7	Step	Solve for y	y = 2x - 8 + 3 y = 2x - 5
8	Step	So, the equation of the line passing through points P(4, 3) and Q(2, -1) is y = 2x - 5
9	SumUp	Can you summarize what you’ve understood in the above steps?
10	Choice.A	Incorrect, the constant term should be negative (-5), not positive (+5)	y = 2x + 5
11	Choice.B	Correct, as explained above	y = 2x - 5
12	Choice.C	Incorrect, it is missing the constant term (-5)	y = 2x
13	Choice.D	Incorrect, it is missing the slope term (2x)	y = 5
14	Answer	Option	B
15	SumUp	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the equation of the line passing through the points P(4,3) and Q(2,-1).

Formula:

We can use the point-slope form of a linear equation

y - y1 = m(x - x1)

Formula:

First, let’s find the slope (m) using the two given points

m = \$(y2 - y1) / (x2 - x1)\$m

Step

Substitute the values into the slope formula and calculate the m

m = \$(-1 - 3) / (2 - 4)\$

m = \$(-4)/(-2)\$

m = \$2\$

Hint

Now that we have the slope (m = 2) and one of the points (P) (x1 = 4, y1 = 3) we can use the point-slope form to write the equation

y - y1 = m(x - x1)

Step

Substitute the values and simplify the equation

y - 3 = 2(x - 4) y - 3 = 2x - 8

Step

Solve for y

y = 2x - 8 + 3

y = 2x - 5

Step

So, the equation of the line passing through points P(4, 3) and Q(2, -1) is y = 2x - 5

SumUp

Can you summarize what you’ve understood in the above steps?

Choice.A

Incorrect, the constant term should be negative (-5), not positive (+5)

y = 2x + 5

Choice.B

Correct, as explained above

y = 2x - 5

Choice.C

Incorrect, it is missing the constant term (-5)

y = 2x

Choice.D

Incorrect, it is missing the slope term (2x)

y = 5

Answer

Option

SumUp

Can you summarize what you’ve understood in the above steps?