Question

The line that passes through (-2, 4) and is parallel to x - 2y= 6

Answer 1

Answer:

The equation of other line parallel to given line is y = $\dfrac{x}{2}$ + 5 .

Step-by-step explanation:

Given as :

The equation of a line is

x - 2 y = 6

Or, 2 y = x - 6

Or, y = $\dfrac{1}{2}$x - $\dfrac{6}{2}$

i.e y = $\dfrac{1}{2}$x - 3

The standard equation of line is given as

y = m x + c

where m is the slope of line

Now, comparing given line with standard line equation

The slope of line x - 2 y = 6 is m =  $\dfrac{1}{2}$

Again

Other line is passing through point (- 2 , 4) and is parallel to given line

For parallel line condition

slope of both lines are equal

Let The slope of other line = M

So, M = m = $\dfrac{1}{2}$

Again

Equation of line with slope $\dfrac{1}{2}$ and passing through point (-2 , 4)

y - $y_1$ = M ( x - $x_1$ )

i.e y - 4 = ($\dfrac{1}{2}$) ( x + 2)

Or, y - 4 = $\dfrac{x}{2}$ + 1

Or, y = $\dfrac{x}{2}$ + 1 + 4

i.e y = $\dfrac{x}{2}$ + 5

Hence, The equation of other line parallel to given line is y = $\dfrac{x}{2}$ + 5 . Answer