[tex]y = 2x - 9[/tex]
Step-by-step explanation:
Let's rewrite the given equation such that only y is on the left side and everything else on the right side:
[tex]3x + 6y = -30 \Rightarrow 6y = -3x - 30[/tex]
Simplifying this by dividing by 6, we get
[tex]y = -\frac{1}{2}x - 5[/tex]
This line has a slope of -1/2, which means that a line perpendicular to this has a slope of 2 (i.e., negative reciprocal). So we can write its equation as
[tex]y = 2x + b[/tex]
This is the slope-intercept form of the equation of the line perpendicular to our given line. To complete this form, we need to find the value of b. Since this line passes through (1, -7), put these numbers into our equation to get
[tex]-7 = 2(1) + b \Rightarrow b = -9[/tex]
Therefore, the slope-intercept form of the equation can be written as
[tex]y = 2x - 9[/tex]
