4) The equation of line p is y=-4x+1 Line q is perpendicular to line p and passes through (-6,1) . What is the equation of line q?

To find the equation of line q, we need to determine its slope and use the point-slope form of a linear equation.Step 1: Find the slope of line p.The equation of line p is given as . The slope of a line in the form is the coefficient of x. Therefore, the slope of line p is -4.Step 2: Determine the slope of line q.Since line q is perpendicular to line p, its slope will be the negative reciprocal of the slope of line p. The negative reciprocal of -4 is .Step 3: Use the point-slope form to find the equation of line q.The point-slope form of a linear equation is given by , where is a point on the line and m is the slope. We are given that line q passes through the point , so we can use this point and the slope we found in step 2.Substituting the values into the point-slope form, we have: Simplifying further: Expanding the right side: Simplifying the fraction: Adding 1 to both sides: Combining like terms: Therefore, the equation of line q is .