⊥ to y = 3x + 1 through (9, 1)

Question

Write an equation in slope intercept form for the given information.

Answer 1

Since you are looking for a perpendicular line, let's find the slope of the new line first. The original slope is 3 so we need the opposite reciprocal of the number 3. "Opposite" means change the sign, so the new slope will be negative. "Reciprocal" mean 'flip' the fraction. Since 3 has the same value as the fraction 3/1, when we flip it, we get 1/3.

Thus, the opposite reciprocal of 3 is -1/3.

m = -1/3

Now that we have the slope, -1/3, and were given a point, (9,1), we can find the new equation by substituting the known quantities into the slope-intercept equation, y=mx+b.

1 = -1/3(9) + b We can solve this equation for b, to determine the y-intercept of the new line

1 = -3 + b Simplify the multiplication

4 = b Add 3 to both sides of the equation

Finally, with a slope of -1/3 and a y-intercept of 4:

y = -1/3x + 4

You can check to see if the answer is correct by substituting the point (9,1) into the equation to see if it yields a true mathematical statement.

1 = -1/3(9) +4 Simplify the multiplication

1 = -3 + 4 Combine Like Terms

1 = 1 Since 1 does, in fact, equal 1... we have an equation that passes through (9,1)

Answer 2

y = -x/3 + b

1 = -9/3 + b

1 = -3 + b

4 = b

y = -x/3 + 4