how do you solve 2x+y=7

Question

 i want to know if it fits the table 

 

x     f(x)

-4    -1

-3     1

-2     3

-1     5

Answer 1

Christia, for this problem let's rearrange the equation to make it a little easier to see if the equation reflects the table. You don't have to do so, but I think it helps.

 

2x+y=7 is given, so if we isolate a variable y would be easier since there is only 1. You must subtract both sides by 2x in order for y to be alone. Here is the math:

 

2x-2x+y=7-2x

y=7-2x or y= -2x+7

 

 

This is telling you that if the equation matches the table, f(x) [which is the same as y] should equal the corresponding x value multiplied by -2 and then adding 7 to the product found. Let's use the first coordinates to illustrate this (-4, -1):

 

y= -2x+7

-1= -2• -4+7

-1= 8+7

-1=15

-1≠15

As you can see, the math shows that y should be 15 if the x coordinate is -4 for the equation y= -2x+7. So the equation does not reflect the table.

Answer 2

2x + y = 7 is an eqn of a straight line

y = -2x +7

with a slope of -2, and an intercept of 7

 

the table is for a straight line with a positive slope of 2

found from e.g. using the first two points in the table: (1 - -1)/(-3 -  -4) = 2

and an intercept of 7

y = 2x + 7 or

-2x + y = 7