Find an equation of the line that satisfies the given conditions. Through (1, 1); parallel to the line y = 2x − 9

Answer 1

Your linear equation, y= 2x-9, is in slope intercept form. This means the 2 in 2x is the slope and that -9 is the y intercept. Really to answer your question you only need to know the slope and the point it goes through.

Keeping in mind that 2 is the slope, you can then use point slope form to answer the question.

y - y₁ = m(x-x₁)

You now just need to fill in the variables y₁, m, and x₁. By definition of a parallel line, your new equation needs to have the same slope as y = 2x - 9. Therefore, your m = 2.

Now, since the line needs to go through (1,1), you can plug in the x and y values into the point slope form with your slope, where x₁=1 and y₁=1. This would lead to your equation looking like this:

y - 1 = 2(x - 1)

You then need to change this to slope intercept form by rearranging the numbers to be in the form of y = mx + b. So, distribute the 2 so that y - 1 = 2x - 2. Then, add the 1 from the left side. Your answer is then this:

y = 2x - 1.

Hope this helps!