Question

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?

Answer 1

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.

Answer 2

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