Write an equation for a line perpendicular to 4 y + 20 x = − 20 and passing through the point (-10,-4)

Answer 1

First, we must simplify the equation of the line you were given. 4y + 20x = -20 simplified by diving by four is y + 5x = -5. Changing that to slope-intercept form by subtracting both sides by 5x, the equation of your line is y = -5x - 5.

A perpendicular line will, by definition, have the negative reciprocal of the slope of the original line, so the slope of the new line is 1/5. Therefore, the second line has an equation of y = 1/5x + b, where b is the intercept. Since we have a point on this second line, we can solve for b (the intercept) by plugging in the x and y values of that point. Thus, -4 = 1/5(-10) + b. Simplifying, -4 = -2 + b, so b = -2. The equation of the second line is y = 1/5x - 2!