The parallel line 3x + y =3, can be write on y-intercept form:
Solve for y the equation:
3x + y = 3
y = 3 -3x
Now, two lines are parallel when they have the same slope. In this case for line y= 3 -3x, the slope is the number with the x.
Therefore, the slope is -3.
Use the slope intercept-form using slope=m=3 and the point (1,-7):
[tex]y-y_1=m(x-x_1)[/tex]
Replace these values and solve for y:
[tex]y-(-7)=-3(x-1)[/tex][tex]y+7=-3x+3[/tex]
Solving for x:
[tex]y=3x+3-7[/tex]
The equation that passes through the point (1,-7) and is parallel to the line3x + y =3 is :
[tex]y=-3x-4[/tex]
