Question

Find the equation of the line that passes through (2,-1) and is parallel to
y
=
4
−
2
x

I am unsure of the answer

Answer 1

Hi student, let me help you out!

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Part 1.

What is the slope of the line [tex]\mathtt{y=4-2x}[/tex]?

- slope = -2

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Part 2.

What is the slope of the line that is parallel to the line [tex]\mathtt{y=4-2x}[/tex]?

- slope = [tex]\mathtt{-2}[/tex]

[tex]\dag\mathtt{Drawing\:Conclusions}[/tex]

The slopes of parallel lines are identical.

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Part 3. Equation

Now that we've found the slope, we can easily find the equation.

Recall the point that the line contains: (2, -1).

Let's stick in its y-coordinate, -1, instead of y: [tex]\mathtt{-1=-2x+b}[/tex]

Do the exact same thing with x: [tex]\mathtt{-1=-2(2)+b}[/tex].

Upon simplifying, we obtain [tex]\mathtt{-1=-4+b}[/tex].

Now we should add 4 to both sides: [tex]\mathtt{-1+4=b}[/tex].

Upon simplifying, we obtain [tex]\mathtt{3=b}[/tex]

- Incase you're wondering, "b" is the y-intercept.

∴, the equation of the line is [tex]\underline{\boxed{\mathtt{y=-2x+3}}}[/tex].

Hope this helped you out, ask in comments if any queries arise.

Best Regards!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\bold{Reach\:Far.\:Aim\:high.\:Dream\:big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{3}}[/tex]

Answer 2

Equation of a line passing through a point
Equation of a line passing through a point

(1,1) is given by −1=(−1)
(
x
1
,
y
1
)
is given by
y
−
y
1
=
m
(
x
−
x
1
)

where m is the slope of the line. We find the slope of the given line.
where m is the slope of the line. We find the slope of the given line.

2+−4=0⟹=−2+4⟹slop of the line = -2
2
x
+
y
−
4
=
0
⟹
y
=
−
2
x
+
4
⟹
slop of the line = -2

Since the two lines are parallel their slopes are equal
Since the two lines are parallel their slopes are equal

Equation of the line passing through (2, -1) with slope -2 is:
Equation of the line passing through (2, -1) with slope -2 is:

+1=−2(−2)
y
+
1
=
−
2
(
x
−
2
)

⟹2++1−4=0
⟹
2
x
+
y
+
1
−
4
=
0

⟹2+−3=0 is the required equation
⟹
2
x
+
y
−
3
=
0
is the required equation

1

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