Given the equation

2x + 5y = 7,

answer the following questions.

(a) Is the slope of the line described by this equation positive or negative?

positive

negative

(b) As x increases in value, does y increase or decrease?

increase

decrease

(c) If x decreases by 5 units, what is the corresponding change in y?

To answer these questions it is easiest first to put the equation in the form y = mx+c. This is done by rearranging to form 5y = - 2x + 7 and then dividing by 5 to form y = - 0.4x + 1.4. Question (a) The slope of this line is negative. The "m" part of the equation describes the gradient of the line which in this case in negative. Question (b) As x increases in value y will decrease as the value of x is multiplied by a negative 2. Question (c) If x decreases by 5 units the value of y will increase by 2 units. This can be tested by inserting values into the equation.

A.

y=mx+b

m=slope

so

2x+5y=7

solve for y

5y=-2x+7

y=-2/5x+7/5

the slope is - 2/5

the slope is negative

b.

lets test them

2x+5y=7

if x=1, y=1

we increase x

if x=2, y=3/5

1>3/5

y decreases

c.

ok

2x+5y=7

if x=5 then y=-3/5

if x=0, then y=7/5

the change is from - 3/5 to 7/5 which is a change of 10/5 or 2

the change in y is 2

a. slope is - 2/5 so negative

b. decrease

c. 2