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Step-4

Title: Slope & Line Segment

Grade: 8-a Lesson: S1-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	m = \$(-1 - 3) / (2 - 4)\$ m = \$-4/-2\$
5	Step	After Simplification m value is	\$2\$
6	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)
7	Step	Substitute the values	y - 3 = 2(x - 4)
8	Step	Now, let’s simplify the equation:	y - 3 = 2x - 8 y = 2x -8 + 3 = 2x -5
9	Step	So, the equation of the line passing through points P(4, 3) and Q(2, -1) is	y = 2x - 5.
10		Answer	B

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

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

m = \$-4/-2\$

Step

After Simplification m value is

\$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

y - 3 = 2(x - 4)

Step

Now, let’s simplify the equation:

y - 3 = 2x - 8

y = 2x -8 + 3 = 2x -5

Step

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

y = 2x - 5.

Answer