To find the equation of the line, we are going to use the point-slope form, which is listed below:
[tex](y - y_1) = m(x - x_1)[/tex]
- [tex](x_1, y_1)[/tex] is a point on the line
- [tex]m[/tex] is the slope of the line
You may notice that we have a point, but no slope is given to us. However, the problem states that the line is parallel to the equation [tex]y = 3x + 7[/tex], which means that it has the same slope as this line, which is 3. (Remember that this line is set up in [tex]y = mx + b[/tex] form, where [tex]m[/tex] is the slope)
Thus, we can now insert our values into the point-slope formula to find the equation of our line.
[tex](y + 1) = 3(x - 4)[/tex]
[tex](y + 1) = 3x - 12[/tex]
[tex]y = 3x - 13[/tex]
The problem made it clear that it didn't want the form [tex]y = 3x - 13[/tex], so let's put it in standard form:
[tex]y = 3x - 13[/tex]
[tex]3x - y = 13[/tex]
The equation of our line is [tex]\boxed{3x - y = 13}[/tex].
