Question

Write the standard form of the equation that passes through the point (-2, 4) and is parallel to x - 2y = 6. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

Answer 1

Answer:

The equation of line passing through point ( - 2 , 4) with slope parallel to given line is   y =  $\dfrac{1}{2}$ x + 5

Step-by-step explanation:

Given as :

The equation of 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

Now, Standard equation of line in slope-intercept form

y = m x + c

where m is the slope of line

And c is the y-intercept

Now, Compare given line with standard line equation

So, The slope of line y = $\dfrac{1}{2}$ × x -  3 = m = $\dfrac{1}{2}$

Again

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

∵ For parallel lines condition

The slope of both lines are equal

Let The slope of other line = M

So, from condition

M = m =  $\dfrac{1}{2}$

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

So, Equation of line in slope-point form

y - $y_1$ = M × (x - $x_1$)

Or, y - 4 =  $\dfrac{1}{2}$ × (x - ( - 2) )

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

Or, y = $\dfrac{1}{2}$ × (x + 2 ) + 4

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

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

∴   y =  $\dfrac{1}{2}$ × x + 1 + 4

i.e y =  $\dfrac{1}{2}$ x + 5

So, Equation of other line  y =  $\dfrac{1}{2}$ x + 5

Hence, The equation of line passing through point ( - 2 , 4) with slope parallel to given line is   y =  $\dfrac{1}{2}$ x + 5 . Answer