Explanation:
since we got a point and actually the slope, we can start with the point-slope form and transform.
you know that the slope-intercept form is
y = ax + b
"a" is the slope, "b" is the y-intercept.
we see therefore, that the slope of the given line is 1/4.
a perpendicular slope (90°) turns the slope fraction upside-down and flips the sign.
so, the perpendicular slope is -4/1 = -4.
the point-slope form is
y - y1 = a(x - x1)
"a" is again the slope (for the new line this is -4), (x1, y1) is a given point. in our case (1, 1).
so, we get
y - 1 = -4(x - 1)
we transform by simplifying :
y - 1 = -4x + 4
y = -4x + 5
y = -4x + 5
is the perpendicular line in slope-intercept form that passes through (1, 1).