4. diego is thinking of two positive numbers. he says, "if we triple the first number and
double the second number, the sum is 34."
a. write an equation that represents this clue. then, find two possible pairs of
numbers diego could be thinking of.

3x + 2y = 34. and two possible pairs of positive numbers are  (x, y) = (10, 2) and (x, y) = (4, 11).

Step-by-step explanation:

 Let the First positive number be x and second positive number be y.

Triple of first number = 3x

double of second number = 2y

According to question,

3x + 2y = 34

Therefore, the equation is 3x + 2y = 34

So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3x + 2y = 34

Now,  3x + 2y = 34

3x = 34 - 2y

Let x = 10 and by substituting its value in above expression,

Therefore first pair (x, y) = (10, 2)

In the same way put x = 4 then,

3x = 34 - 2y

Therefore first pair (x, y) = (4, 11)

Therefore, (x, y) = (4, 11) and  (x, y) = (10, 2) are the two possible pairs of numbers Diego could be thinking of as these both values satisfy the equation 3x + 2y = 34.  

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.