How do you find a parallel aandmd perpendicular line using a graph

The problem asks for the equations of the lines, so you use the information given in the graph to help you write the equations.

The given line has a "rise" of -4 for a "run" of 1, hence a slope of -4/1 = -4. This is the information you need from that line to write the equations of lines through the given point, (4, 3).

(a) The parallel line will have the same slope. You are asked for "an equation", so the simplest is to provide the necessary equation in point-slope form.

The equation of a line with slope m through point (h, k) is ...

... y - k = m(x - h)

For m = -4, (h, k) = (4, 3) your parallel line is ...

... y - 3 = -4(x -4)

(b) The perpendicular line will have a slope that is the negative reciprocal of that of the given line: -1/-4 = 1/4. Using the same point-slope form, your perpendicular line has equation ...

... y - 3 = (1/4)(x - 4)

36 is the final answer! : )