Some terminology:
⇒what is the slope
⇒ is the steepness of the line
⇒calculated by dividing the rise over the run
⇒ rise is the change in the y-direction
⇒ run is the change in the x-direction
⇒look at the diagram I attached
⇒ how to find the slope in a linear equation
⇒look to the coefficient of the 'x' variable
⇒ that is the slope
Ex. For the line y = x, the slope is 1
⇒A line with a positive slope rises from left to right while a line with a negative slope falls from left to right.
Ex. y=x has a positive slope and thus is rising
We want to find the equation that could represent the blue line
⇒ let's look into each equation and see whether they work or not
First case: [tex]y = -x[/tex]
⇒The equation given has the line falling, when the graph in the
equation is rising
⇒ not the answer
Second case: [tex]y=2x[/tex]
⇒ the equation given has the line that has a bigger slope than the
the equation shown, which has a smaller slope than y = x
⇒ not the answer
Third case: [tex]y=\frac{1}{2}x[/tex]
⇒ the equation given fits the requirement of having a rising slope that
is smaller than y = x
⇒ is a possible answer
Fourth case: [tex]y = 0.001x[/tex]
⇒ the equation given has a slope that is almost horizontal when the
line shown in the graph doesn't
⇒ not the answer
Thus after examing all the choices:
⇒ Answer: [tex]y=\frac{1}{2}x[/tex]
