Submit Answer 11. [-/1 Points] DETAILS KMBIALG7 3.5.051. MY NC Write the slope-intercept equation of the line that passes through the given point and is perpendicular to the given line. \[ (0,0), y=6 x-7 \] Need Help? Read It Submit Answer 12. $[1 / 1$ Points] DETAILS PREVIOUS ANSWERS KMBIALG7 3.5.067.MI. Write an equation of the line with the following properties. Write the equation in slope-intercept form.
Solution
Step 1 ：The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 ：The given line is \(y = 6x - 7\), so its slope is 6.
Step 3 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line perpendicular to the given line is \(-1/6\).
Step 4 ：The line passes through the origin (0,0), so its y-intercept is 0.
Step 5 ：Substituting the slope and y-intercept into the slope-intercept form gives the equation of the line as \(y = -1/6x + 0\), which simplifies to \(y = -1/6x\).
Step 6 ：\(\boxed{y = -\frac{1}{6}x}\) is the slope-intercept equation of the line that passes through the origin (0,0) and is perpendicular to the line \(y = 6x - 7\).
