The equations of parallel lines have the same slope or rates.
The equation of the line parallel to [tex]\mathbf{6x + 7y = -49}[/tex] is [tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
The equation is given as:
[tex]\mathbf{6x + 7y = -49}[/tex]
Make 7y the subject
[tex]\mathbf{7y = -6x-49}[/tex]
Make y the subject
[tex]\mathbf{y = -\frac{6}{7}x -7}[/tex]
A linear equation is represented as:
[tex]\mathbf{y =mx + b}[/tex]
Where m represents the slope.
So, we have:
[tex]\mathbf{m = -\frac 67}[/tex]
Parallel lines have the same slope.
So, the slope of the line is [tex]\mathbf{m = -\frac 67}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
Substitute [tex]\mathbf{m = -\frac 67}[/tex]
[tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
Hence, the equation of the line parallel to [tex]\mathbf{6x + 7y = -49}[/tex] is [tex]\mathbf{y = -\frac 67(x - x_1) + y_1}[/tex]
Read more about parallel lines at:
https://brainly.com/question/402319
