Question

Find the equation of the line that passes through (-1,2) and is perpendicular to y=1 – 2x.
Leave your answer in the form y = mx + c

Answer 1

Answer:

The equation of the line that passes through (-1,2) and is perpendicular to y=1-2x is $\mathbf{y=\frac{1}{2} x+\frac{5}{2}}$

Step-by-step explanation:

We need to write the equation of the line that passes through (-1,2) and is perpendicular to $y=1 - 2x$

The equation must be in form  $y=mx+c$ has m equals to slope and c equals to y-intercept

So, we need to find slope and y-intercept.

Finding Slope

When the lines are perpendicular there slopes are opposite to each other.

Slope of given equation is:

$y=1 - 2x$

We can write it as: $y=-2x+1$

Comparing it with  $y=mx+c$ we get m = -2

Now, The slope of given equation is: m = -2

The slope of required equation will be: m=$\frac{1}{2}$

Finding y-intercept

Using point (-1,2) and slope m=$\frac{1}{2}$, we can find y-intercept

$y=mx+c\\2=\frac{1}{2} (-1)+c\\2=-\frac{1}{2} +c\\c=2+\frac{1}{2} \\c=\frac{4+1}{2}\\ c=\frac{5}{2}$

So, y-intercept is: c = $\frac{5}{2}$

Equation of line

Now, the equation of line having slope m=$\frac{1}{2}$  and c = $\frac{5}{2}$ is:

$y=mx+c\\y=\frac{1}{2} x+\frac{5}{2}$

So, the equation of the line that passes through (-1,2) and is perpendicular to y=1-2x is $\mathbf{y=\frac{1}{2} x+\frac{5}{2}}$

Answer 2

The equation of required line is $y=\dfrac{1}{2}x+\dfrac{5}{2}$.

Given:

A line passes through $(-1,2)$ and is perpendicular to $y=1-2x$.

To find:

The equation of the line.

Explanation:

We have,

$y=1-2x$

On comparing this equation with $y=mx+c$, we get

$m=-2$

So, the slope of the given equation is $-2$.

The product of slopes of two perpendicular lines is always $-1$.

$m_1\times m_2=-1$

$-2\times m_2=-1$

$m_2=\dfrac{-1}{-2}$

$m_2=\dfrac{1}{2}$

The slope of the required line is $\dfrac{1}{2}$ and it passes through the point $(-1,2)$. So, the equation of the line is:

$y-2=\dfrac{1}{2}(x-(-1))$

$y-2=\dfrac{1}{2}(x+1)$

$y=\dfrac{1}{2}x+\dfrac{1}{2}+2$

$y=\dfrac{1}{2}x+\dfrac{5}{2}$

Therefore, the equation of required line is $y=\dfrac{1}{2}x+\dfrac{5}{2}$.

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