SOLUTION: solve each system by graphing y=-2/3+2 y=-2x-2 I have the answer (-3,4) so thats -3 x axis positive 4 (up on y axis) unsure how to express this in a graph do I need additio

Algebra ->  Graphs -> SOLUTION: solve each system by graphing y=-2/3+2 y=-2x-2 I have the answer (-3,4) so thats -3 x axis positive 4 (up on y axis) unsure how to express this in a graph do I need additio      Log On


   

Question 723128: solve each system by graphing
y=-2/3+2
y=-2x-2 I have the answer (-3,4) so thats -3 x axis positive 4 (up on y axis)
unsure how to express this in a graph do I need addition points to show where the line goes?
thank you so much
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe the first equation was meant to be y=-%282%2F3%29x%2B2 so that is how I will solve it.

You are expected to find the answer from the graph, so pretend you do not know the answer.

y=-%282%2F3%29x%2B2 and y=-2x-2 are linear equations that graph as straight lines, and are given in slope-intercept form.
For y=-%282%2F3%29x%2B2 , the slope is -%282%2F3%29 and the intercept is 2.
For y=-2x-2 , the slope is -2 and the intercept is -2.
When the equation is in the y= ... slope-intercept from, the number multiplying the x is the slope and the number added at the end is the intercept, or y-intercept (the y-coordinate of the point where the line crosses the y-axis).

We plot the y- intercepts first. Then we use the slope to go from that point to another point,and repeat the procedure as needed/desired to help us draw the line. No calculations, just counting.

Graphing y=-2x-2 :
A slope of -2 means that for every 1 unit increase in x, y increases by -2 (meaning that it decreases by 2 units).
So from (0,-2), the intercept point for y=-2x-2 , we move one unit right and 2 down to mark the next point. We repeat that procedure for the next and the next points. Finally we draw a line through our points.


Adding the line for y=-%282%2F3%29x%2B2 to the graph:
A slope of -%282%2F3%29 means that the ratio of increase in to to increase in x is -%282%2F3%29 , meaning that for every 3 unit increase in x, y increases by -2 (it decreases by 2 units).
So from (0,2), the intercept point for y=-%282%2F3%29x%2B2 , we move 3 unit right and 2 down to mark the next point. Those two points are far enough apart to allow us to draw the line accurately, so we draw a line through our points.

The two lines seem to intersect at point (-3,4), corresponding to highlight%28x=-3%29 and highlight%28y=4%29 .
We must verify, because drawings can be inaccurate.
If that pair of values satisfies both equations, it is the solution of the system, found by graphing.
Substituting x=-3 into y=-%282%2F3%29x%2B2 we get
y=-%282%2F3%29%28-3%29%2B2 --> y=2%2B2 --> y=4
Substituting x=-3 into y=-2x-2 we get
y=-2%28-3%29-2 --> y=6-2 --> y=4
THE SOLUTION IS VERIFIED.