Points: 2 of 2

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Perpendicular to the line $x-11 y=-1$; containing the point $(0,7)$

The equation of the line is $y=-11 x+7$.
(Simplify your answer.)

Step 1 ：The given line is in the form of \(ax+by=c\). We can convert it to the slope-intercept form \(y=mx+c\) to find the slope of the given line.

Step 2 ：The slope of the given line is \(\frac{1}{11}\).

Step 3 ：The slope of a line perpendicular to this line would be the negative reciprocal of the slope of the given line, which is -11.

Step 4 ：We can then use the point-slope form of the line equation \(y-y_1=m(x-x_1)\) to find the equation of the line perpendicular to the given line and passing through the given point.

Step 5 ：Substituting the values, we get the equation of the line as \(11x + y - 7 = 0\).

Step 6 ：Final Answer: The equation of the line is \(\boxed{11x + y - 7 = 0}\).