SOLUTION: "The line is perpendicular to y=2x-4 and passes though (4,7)" Could you plese show me the formula on how to get the answer in y=mx+b form?

Algebra ->  Linear-equations -> SOLUTION: "The line is perpendicular to y=2x-4 and passes though (4,7)" Could you plese show me the formula on how to get the answer in y=mx+b form?      Log On


   

Question 366334: "The line is perpendicular to y=2x-4 and passes though (4,7)"
Could you plese show me the formula on how to get the answer in y=mx+b form?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know that I can show you a "formula" but I can show you a procedure.
You want your answer to be an equation in the slope-intercept form:
y+=+mx%2Bb of a line that is perpendicular to the line y+=+2x-4 and which passes through the point (4, 7).
Let's start with the slope:
If two lines are perpendicular, their slopes are the negative reciprocal of each other.
The given line is: highlight%28y+=+2x-4%29. Since this is in the slope-intercept form: y+=+mx%2Bb you can see that the slope m+=+2.
The negative reciprocal of 2 is -1%2F2.
So you can start with:
y+=+%28-1%2F2%29x%2Bb but now you need to find the value of b, the y-intercept.
So we substitute the x- and y-coordinate values of the given point (4, 7) into the equation above and solve for b.
7+=+%28-1%2F2%29%284%29%2Bb Simplify this:
7+=+-2%2Bb Add 2 to both sides.
9+=+b Now that we have the value of b, we can write the final equation.
highlight_green%28y+=+%28-1%2F2%29x%2B9%29
And just to show you what these look like when graphed:
graph%28400%2C400%2C-5%2C20%2C-5%2C20%2C2x-4%2C%28-1%2F2%29x%2B9%29