Gradient??????????????

How would you plot these co-ordinates on a graph and where would they meet eachother??????????????





1. y= 2x + 5





2. y= - 2/3x -3





(I know how to plot number one, but not number two. How do you plot 2/3 on a graph!!???)Gradient??????????????
Gradient is rise over run, so for your first one, it rises by 2, and runs across 1 (2/1)





For your second one, it rises by 2, and runs by 3 (2/3)


However, since it is negative, you have to make it go down by 2 instead. (Since it is negative, your line should be going in a direction like this: \ )





If you draw the graph correctly, the points should intersect at (-3,-1)Gradient??????????????
remember that slope is rise over run ... (delta Y) / (delta X)





so for every -2 (2 down) you go 3 to right


[ or for every 2 up, you go 3 to left... either is correct]





1st step ... figure out the Y intercept ...(b)


eq1 = 5 (0,5)


eq2 = -3 (0,-3)





next is figure where they intersect....


2x +5 = -2/3x -3





2 2/3x = -8


8/3x = -8


(3/8) 8/3x = -8 (3/8)


x = -3





when x = -3 .... 2(-3) + 5 = -1


.........x = -3 .. -2/3(-3) -3 = -(-2) -3 = -1





intersection point is (-3,-1)





now connect the b's to the intersection point





eq1 connects (0,5) to (-3,-1)


eq2 connects (0,-3) to (-3,-1)
to plot the second one you need two points of the function:


for example x=0 yields y=-3 and for x=3 y=-5; you draw the line that contains these two points and you've got the Plot.


The point of intersection is:


2x+5=-2/3x-3


8/3 x = - 8


x= -8 * 3 / 8 = -3


y = -1
Well, they ';meet'; or intersect whenever they are equal. We can find where they intersect by setting the two equations equal to each other and solve for x.





2x+5=-(2/3)x-3





2x+2/3x=-8


8/3x=-8


x=-1/3





To plot: Use parenthesis:


-(2 / 3 )*x-3