Question

X-2y=4 going through (1,-6)

Answer 1

Answer:

A.

y

=

−

2

x

−

3

.

Explanation:

First, rewrite the equation in slope-intercept form:

y

=

m

x

+

b

.

−

x

+

2

y

=

4

⇒

2

y

=

x

+

4

⇒

y

=

1

2

x

+

2

So the slope of the given line is

m

=

1

2

.

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope

m

, then a line perpendicular to this has slope

m

*

=

−

1

m

. That means the slope of our perpendicular line is

m

*

=

−

1

1

/

2

=

−

2

.

Knowing the new slope and a point, we can find an equation for our perpendicular line by using the slope-point equation

y

−

y

1

=

m

(

x

−

x

1

)

, or by plugging in the given

(

x

,

y

)

point (and the new slope

m

*

) into

y

=

m

x

+

b

to find

b

for the new line.

y

−

y

1

=

m

(

x

−

x

1

)

⇒

y

−

1

=

−

2

[

x

−

(

−

2

)

]

⇒

y

−

1

=

−

2

[

x

+

2

]

⇒

y

=

−

2

x

−

3

or

y

=

m

x

+

b

⇒

1

=

−

2

(

−

2

)

+

b

⇒

1

=

4

+

b

⇒

b

=

−

3

∴

y

=

m

x

+

b

becomes

y

=

−

2

x

−

3

.

Step-by-step explanation:

Answer 2

Answer:

false

Step-by-step explanation:

Okay so we plug in the values for x and y to make the equation:

1 - 2 x -6 = 4

And then we just solve the left side:

2 x -6 = -12

1 - -12 = 1 + 12 = 13

So this is false