Question

Line l passes through the points (1, 3) and (2, 5), and

Answer 1

Answer:

-3

Step-by-step explanation:

I'm going to find both equations first.

Slope for line l can be found by doing

 (1  ,  3)

- (2 ,  5)

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  -1      -2          so slope is -2/-1 or just 2

y=mx+b is a linear equation with slope m and y-intercept b

y=2x+b  now we need b

3=2(1)+b  plug in a point on the line

3=2+b

so b=1

The equation for line l is y=2x+1

The other equation line m has the slope given which is 1 so this equation will be of the form y=1x+b

to find this b (this y-intercept) use the point that you know is on the line

4=1(1)+b  

so b=3

so line m is y=1x+3 or y=x+3

So we want to find when y=2x+1 and y=x+3 intersect

Replace first y with the 2nd y which is x+3

x+3=2x+1

subtract x on both sides

  3= x+1

subract 1 on both sides

 2=x

 x=2

y=2x+1

y=2(2)+1

y=4+1

y=5

So the intersection is (2,5)

So a=2 and b=5

a-b =2-5=-3