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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

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Part 1.

What is the slope of the line $$\mathtt{y=4-2x}$$?

- slope = -2

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Part 2.

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

- slope = $$\mathtt{-2}$$

$$\dag\mathtt{Drawing\:Conclusions}$$

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: $$\mathtt{-1=-2x+b}$$

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

Upon simplifying, we obtain $$\mathtt{-1=-4+b}$$.

Now we should add 4 to both sides: $$\mathtt{-1+4=b}$$.

Upon simplifying, we obtain $$\mathtt{3=b}$$

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

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

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

Best Regards!

$$\star\bigstar\underline{\underline{\overline{\overline{\bold{Reach\:Far.\:Aim\:high.\:Dream\:big.}}}}}\bigstar\star$$

$$\underline{\rule{300}{3}}$$
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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