The economy of India is a developing mixed economy. It is the world's sixth-largest economy by nominal GDP and the third-largest by purchasing power parity (PPP).

4 0

3 years ago

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

egoroff_w [7]

Answer:

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

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

Determine the slope (m):

$y = 1 -2x$

Rearrange into slope-intercept form:

$y = -2x+1$

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of $\displaystyle\frac{1}{2}$ . Plug this into $y=mx+b$ :

$y=\displaystyle\frac{1}{2} x+b$

Determine the y-intercept (b):

$y=\displaystyle\frac{1}{2} x+b$

Plug in the given point (1,3) and solve for b:

$3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}$

Therefore, the y-intercept is $\displaystyle \frac{5}{2}$ . Plug this back into $y=\displaystyle\frac{1}{2} x+b$ :

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

I hope this helps!

8 0

2 years ago