SOLUTION: I am supposed to write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of each equation. (1,-3), y=1/2x+4

Algebra ->  Points-lines-and-rays -> SOLUTION: I am supposed to write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of each equation. (1,-3), y=1/2x+4      Log On


   

Question 175244This question is from textbook Algebra 1
: I am supposed to write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of each equation.
(1,-3), y=1/2x+4 This question is from textbook Algebra 1

Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
First thing is to remember that perpendicular lines have slopes that are negative reciprocals. That is to say that if L%5B1%5D has a slope m%5B1%5D and L%5B2%5D has a slope m%5B2%5D then L%5B1%5D is perpendicular to L%5B2%5D if and only if m%5B1%5D=%28-1%29%2Fm%5B2%5D.

The slope of your given line is already in slope-intercept form, so you can see that the slope of the given line is 1%2F2 because 1%2F2 is the coefficient on the x term. That means that the slope of any line perpendicular to the given line must be %28-1%29%2F%281%2F2%29=-2.

Knowing the slope and a point, you can use the point-slope form of a line to create the desired equation. The point slope form is: y-y%5B1%5D=m%28x+-+x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) are the coordinates of the given point.

Just plug in the numbers and then solve the resulting equation for y to put the equation into slope-intercept form.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When an equation has the form
y+=+mx+%2B+b, m is the slope of the line
y+=+%281%2F2%29%2Ax+%2B+4 1%2F2 is the slope of this line
You are asked to find a line that is perpendicular to this
one. A line that is perpendicular to another line will
have a slope that is m%5Bp%5D+=+-%281%2Fm%29, so in your case
m%5Bp%5D+=+-%281%2F%281%2F2%29%29
m%5Bp%5D+=+-2
Also given is the point (1,-3) that the line must pass through
The general form of the slope-intercept equation is:
%28y+-+y%5B1%5D%29%2F%28x+-+x%5B1%5D%29+=+m, so, filling in the given data:
%28y+-+%28-3%29%29%2F%28x+-+1%29+=+-2
%28y+%2B+3%29%2F%28x+-+1%29+=+-2 answer