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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Perpendiculer Lines

Grade: 6-a Lesson: S2-L8

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 (8, −2) and perpendicular to 2x + 6y = 1.
2	Step	The given values are	⇒ \$"x"_1 = 8\$ ⇒ \$"y"_1 = -2\$ ⇒ equation = 2x + 6y = 1
3	Formula	To find its slope, we can rewrite it in the slope-intercept form	⇒ y = mx + b where m = slope
4	Step	Rewrite the equation in the form of slope-intercept form	6y = −2x + 1
5	Step	After simplification	⇒ \$"y" = (-2/6) "x" + 1/6\$ ⇒ \$"y" = (-1/3) "x" + 1/6\$
6	Hint	So, the slope of the given line is \$-1/3\$.
7	Formula	The slope-point form of the equation of a line:	\$"y" − "y"_1 = "m"("x" − "x"_1\$)
8	Step	Plugging in the values in the formula	y − (−2) = 3(x − 8)
9	Step	Simplify the equation	y + 2 = 3x - 24
10	Step	Now, isolate y	y = 3x − 26
11	Step	So, the equation of the line passing through (8, −2) and perpendicular to 2x + 6y = 1 is y = 3x − 26.
12	SumUp	Can you summarize what you’ve understood in the above steps?
13	Choice.A	This is correct because it have the correct slope for a line perpendicular to the given line	y = 3x − 26
14	Choice.B	This is not correct because it does not have the correct slope for a line perpendicular to the given line	y = x − 26
15	Choice.C	This is not correct because it has a positive slope, while we need a line with a slope of 3	y = 3x + 26
16	Choice.D	This is not correct because it does not have the correct slope for a line perpendicular to the given line	y = x + 26
17	Answer	Option	A
18	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 (8, −2) and perpendicular to 2x + 6y = 1.

Step

The given values are

⇒ \$"x"_1 = 8\$
⇒ \$"y"_1 = -2\$
⇒ equation = 2x + 6y = 1

Formula

To find its slope, we can rewrite it in the slope-intercept form

⇒ y = mx + b
where m = slope

Step

Rewrite the equation in the form of slope-intercept form

6y = −2x + 1

Step

After simplification

⇒ \$"y" = (-2/6) "x" + 1/6\$
⇒ \$"y" = (-1/3) "x" + 1/6\$

Hint

So, the slope of the given line is \$-1/3\$.

Formula

The slope-point form of the equation of a line:

\$"y" − "y"_1 = "m"("x" − "x"_1\$)

Step

Plugging in the values in the formula

y − (−2) = 3(x − 8)

Step

Simplify the equation

y + 2 = 3x - 24

Step

Now, isolate y

y = 3x − 26

Step

So, the equation of the line passing through (8, −2) and perpendicular to 2x + 6y = 1 is y = 3x − 26.

SumUp

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

Choice.A

This is correct because it have the correct slope for a line perpendicular to the given line

y = 3x − 26

Choice.B

This is not correct because it does not have the correct slope for a line perpendicular to the given line

y = x − 26

Choice.C

This is not correct because it has a positive slope, while we need a line with a slope of 3

y = 3x + 26

Choice.D

This is not correct because it does not have the correct slope for a line perpendicular to the given line

y = x + 26

Answer

Option

SumUp

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