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
Lines l and m intersect at point (2, 5)
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
Line l passes through the points (1, 3) and (2, 5), hence its equation is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1 )\\\\y-3=\frac{5-3}{2-1}(x-1)\\\\y-3=2x-2\\\\2x-y=-1[/tex]
2x - y = -1 (1)
Line m passes through point (1, 4) and has a slope of 1, hence:
[tex]y-y_1=m(x-x_1)\\\\y-4=1(x-1)\\\\x-y=-3[/tex]
x - y = -3 (2)
To determine point (a, b) we solve equation 1 and 2 simultaneously to get:
x = 2, y = 5
Hence lines l and m intersect at point (2, 5)
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