Question

Find the equation of the line that passes through (-1,2) and is perpendicular to y=1 – 2x.

Answer 1

Answer:

is the line are perpendicular then the product of there slope is -1

the slope of the first equation is 2

Step-by-step explanation:

m1+m2=-1

2+m2=-1

m2=-1-2

m2=-3

so the second equation became y=-3x+C

then insert the point (-1,2)

2=-3*-1+C

2=3+C

C=2-3

C=-1

so y=-3x-1

Answer 2

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