Question

Write the equation of a line that is parallel to Y=

Answer 1

Answer:

The slope has to be the same so adjust the y-intercept.

Step-by-step explanation:

y=1/2x-10.5

Answer 2

Answer:

Equation of a line that is parallel to $y=\frac{1}{2} x$

and that passes through the point (9 -6) is $\bold{y=\frac{1}{2} x+\frac{21}{2}}$

 Solution:

The slope - intercept form equation of line is given as

$\bold{y=mx+c}$  --- (1)

Where m is the slope of the line. The coefficient of “x” is the value of slope of the line.

Given that

$y=\frac{1}{2} x$  ---- (2)

On comparing equation (1) and (2) we get slope of equation (2) is $m = \frac{1}{2}$

Consider equation of the line which is parallel to equation (1) is

$y=m_{1} x+b$ --- (3)

If two lines are parallel then slope of both lines should be equal. That is if slope of the line (1) is $\frac{1}{2}$ ,then slope of equation (3) is $m_{1}=\frac{1}{2}$

On substituting value of m1 in equation (3), we get

$y=\frac{1}{2} x+b$  --- (4)

Given that equation (4) passes through (9, -6) that is x = 9 and y = -6. So on substituting value of x and y in equation (4),

$-6=\frac{9}{2}+b$

On simplifying above equation,

$b=\frac{9}{2}+6$

$b=\frac{9+12}{2}$

$b=\frac{21}{2}$

On substituting value of b in equation (4),

$y=\frac{1}{2} x+\frac{21}{2}$

Hence equation of a line that is parallel to $y=\frac{1}{2} x$ and that passes through the point (9 -6)  is $\bold{y=\frac{1}{2} x+\frac{21}{2}}$