Respuesta :
Given:
The given equation of line is
[tex]y=-\dfrac{6}{7}x+3[/tex]
To find:
The equation of line that passes through (-5,4) and is parallel to the given line.
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex] ...(i)
where, m is slope and b is y-intercept.
We have,
[tex]y=-\dfrac{6}{7}x+3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{6}{7}[/tex]
Slope of given line is [tex]m=-\dfrac{6}{7}[/tex].
Slope of parallel lines are same. So, slope of parallel line is [tex]m=-\dfrac{6}{7}[/tex].
The required line passes through (-5,4) with slope [tex]m=-\dfrac{6}{7}[/tex]. So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=-\dfrac{6}{7}(x-(-5))[/tex]
[tex]y-4=-\dfrac{6}{7}(x+5)[/tex]
[tex]y-4=-\dfrac{6}{7}x-\dfrac{30}{7}[/tex]
Adding 4 on both sides, we get
[tex]y=-\dfrac{6}{7}x-\dfrac{30}{7}+4[/tex]
[tex]y=-\dfrac{6}{7}x+\dfrac{-30+28}{7}[/tex]
[tex]y=-\dfrac{6}{7}x-\dfrac{2}{7}[/tex]
Therefore, the correct option is a.
