Write the slope intercept form of a line which passes through the point (7,1) and is perpendicular to the line y= -2x +4

Answer 1

We just need 2 parameters for the line - the slope and the y-intercept. To determine the slope, we take the negative reciprocal of the indicated line:

m=-2

Therefore, the slope of our line is -1/(-2)=1/2

Recalling that the the slope-intercept form of a line is y=mx+b, we can simply substitute the point (7,1) into that equation with 1/2 as the slope and solve for b.

1=(1/2)*7 +b

1=7/2+b

Subtracting 7/2 from both sides, we find b.

b=-5/2

So, finally, our line is:

y=(1/2)x - 5/2

Answer 2

Ok, so we know that if line1 is perpendicular to line 2, then the slope of line 2 is a negative reciprocal of line 1. So we know that the negative reciprocal of -2 is 1/2. So 1/2 is our slope. So now we also now that since it goes through (7,1), then we know that:

1= 1/2*(7) + b

And then we do some algebra.

1=7/2+b

1-7/2=b is the same as:

2/2-7/2=-5/2

So now when we plug in -5/2 for b and check our problem, we get:

1= 1/2*(7) - 5/2

1=7/2-5/2

So the equation for a line that goes through (7,1) and is perpendicular to the line y= -2x+4 is:

y=1/2*x -5/2