20.What is the equation of the line that is perpendicular to y=-4x+1 and passes through the point (2,2)

To find the equation of the line that is perpendicular to $y=-4x+1$ and passes through the point $(2,2)$, we need to follow these steps:<br /><br />1. Find the slope of the given line.<br />2. Find the slope of the perpendicular line.<br />3. Use the point-slope form to find the equation of the perpendicular line.<br /><br />Step 1: Find the slope of the given line.<br />The given line is in the form $y=mx+b$, where $m$ is the slope. Therefore, the slope of the given line is $-4$.<br /><br />Step 2: Find the slope of the perpendicular line.<br />The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Therefore, the slope of the perpendicular line is $\frac{1}{4}$.<br /><br />Step 3: Use the point-slope form to find the equation of the perpendicular line.<br />The point-slope form of a line is given by $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Substituting the values, we get:<br />$y-2=\frac{1}{4}(x-2)$<br /><br />Simplifying the equation, we get:<br />$y-2=\frac{1}{4}x-\frac{1}{2}$<br />$4y-8=x-2$<br />$4y=x-6$<br />$x-4y=2$<br /><br />Therefore, the equation of the line that is perpendicular to $y=-4x+1$ and passes through the point $(2,2)$ is $x-4y=2$.