What is the equation of the line that passes through the point ( 1 , -1 ) and has a slope of -2?

Answer 1

I know of two formulas that you can use to solve this problem. I recommend picking whichever one seems easier to you and sticking with it.

(1) y = mx + b

Using this formula you plug the values in directly for y, m, and x and solve for b, before reconstructing the formula. This has the benefit of being only a single formula to memorize, but you have to remember to do a second step.

(1a) -1 = -2 * 1 + b

-1 = -2 + b (add 2 to both sides)

1 = b

(1a) final answer: y = -2x + 1

Or the other way of solving it is to plug the values into the point-slope formula:

(2) y - y₁ = m * (x - x₁)

This has the advantage of doing everything in a single step, but being a very specific formula for a very specific use.

(2a) y - (-1) = -2 * (x - 1)

(2b) y + 1 = -2x + 2 on the left simplify the double negative, and on the right distribute the negative 2 to both x and -1.

(2c) y = -2x + 1 subtract one from both sides.

Thus both methods give you the same answer, just find a strategy that works well for you and stick with it.

Answer 2

Hi Michelle!

The first step in this problem is to identify that form of our answer will be y = mx +b where m is the slope and b is the y intercept. Since we are already given the slope is -2, we know what m is! That means we have y=-2x+b. From there, we need to figure out b since the "X" is what we will plug in and "y" is the result of what we plug in. The problem gives us a combination of x and y values of (1,-1) where 1 is X since it is the first number and Y is -1 since it is the second number. Plugging those into the equation so far gives -1=-2 * 1+ b

Solving for b by subtracting -2 will give +1 for b. Overall, that gives us y = -2x +1!