Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 1/2 yard long. How many pieces of string does Ms.
2 answers:
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An equation of the form ax+by+c=0, where x, y are variable, and a, b, c are numbers, is called a "linear equation"
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
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-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
-------------------------------------------------------------------------------------------------
-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.