write an equation in slope-intercept form for the line that passes through (4,1) and is perpendicular to 4x-y=3

Question

write an equation in slope-intercept form for the line that passes through (4,1) and is perpendicular to 4x-y=3

Answer 1

Because the given line's equation is in general form, Ax + By = C, we can write the equation of a line perpendicular to that one in general form also, by switching the coefficients of x and y, and switching the sign of one of them. (That will give us a line with the opposite reciprocal slope.)

So our line's equation can be written as x + 4y = C. Since it must pass thru (4,1) we use that to solve for C:

4 + 4(1) = C ; C = 8

Finally, we have x + 4y = 8 which we manipulate to put into the requested slope-intercept form:

4y = - x + 8

y = - 1/4 x + 2