Which graphs below have a domain of all real numbers? Which have a range of all real numbers? Which are functions?
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An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.
They are called "linear" because if we draw all the solutions of such an equation, they form a line.
This also means that it is enough to:
1. find to solutions
2. plot them on the coordinate axis
3.join those 2 points
and all the solutions of the equation y=ax+b will be on that line.
Thus, to draw line y=-3x+3
let x=0, then y=3, so one solution is (0, 3)
let y=0, then x=1 so a second solution is (1, 0)
(remark we can pick x or y to be any value, then solve for the other)
to draw the second line y=2x-7
let x=0, then y=-7
let x=3, then y=-1
plot these points and join them as shown in the picture.
The solution of the system is the point where the lines intersect, which is
(2, -3)
They are called "linear" because if we draw all the solutions of such an equation, they form a line.
This also means that it is enough to:
1. find to solutions
2. plot them on the coordinate axis
3.join those 2 points
and all the solutions of the equation y=ax+b will be on that line.
Thus, to draw line y=-3x+3
let x=0, then y=3, so one solution is (0, 3)
let y=0, then x=1 so a second solution is (1, 0)
(remark we can pick x or y to be any value, then solve for the other)
to draw the second line y=2x-7
let x=0, then y=-7
let x=3, then y=-1
plot these points and join them as shown in the picture.
The solution of the system is the point where the lines intersect, which is
(2, -3)