Respuesta :
Answer:
The equation of line passing through point ( - 2 , 4) with slope parallel to given line is y = [tex]\dfrac{1}{2}[/tex] x + 5
Step-by-step explanation:
Given as :
The equation of line is x - 2 y = 6
Or, 2 y = x - 6
Or, y = [tex]\dfrac{1}{2}[/tex] × x - [tex]\dfrac{6}{2}[/tex]
i.e y = [tex]\dfrac{1}{2}[/tex] × 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 = [tex]\dfrac{1}{2}[/tex] × x - 3 = m = [tex]\dfrac{1}{2}[/tex]
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 = [tex]\dfrac{1}{2}[/tex]
Now, equation of line passing through point ( - 2 , 4) with slope [tex]\dfrac{1}{2}[/tex]
So, Equation of line in slope-point form
y - [tex]y_1[/tex] = M × (x - [tex]x_1[/tex])
Or, y - 4 = [tex]\dfrac{1}{2}[/tex] × (x - ( - 2) )
Or, y - 4 = [tex]\dfrac{1}{2}[/tex] × (x + 2 )
Or, y = [tex]\dfrac{1}{2}[/tex] × (x + 2 ) + 4
Or, y = [tex]\dfrac{1}{2}[/tex] × x + [tex]\dfrac{1}{2}[/tex] × 2 + 4
Or, y = [tex]\dfrac{1}{2}[/tex] × x + [tex]\dfrac{2}{2}[/tex] + 4
∴ y = [tex]\dfrac{1}{2}[/tex] × x + 1 + 4
i.e y = [tex]\dfrac{1}{2}[/tex] x + 5
So, Equation of other line y = [tex]\dfrac{1}{2}[/tex] x + 5
Hence, The equation of line passing through point ( - 2 , 4) with slope parallel to given line is y = [tex]\dfrac{1}{2}[/tex] x + 5 . Answer
