Question

Two linear functions are displayed. Function One is represented by the graph:

The second linear function is y = -4x. Which statement is true about the slope of the two functions?


A) The slope of function one is positive and the slope of function two is negative.

B) Both functions have a negative slope.

C) Both functions have a positive slope.

D) Both functions have the same slope.

Answer 1

Option A

Explanation:

Function One is represented by the graph. We can see that the slope of the First Function is positive because the formula of slope is

`Slope=(Change\ in\ y)/(Change\ in\ x) \\\\`

And we can see that in the graph the change in y and change in x are both positive as the function is increasing because if we see the graph closely,

When x = 1 the value of y = 2 and when x = 2 the value of y = 4 and when x = 3 the value of y = 6 so the values are increasing of x and of y hence the slope is positive and the value of slope is 2.

Now the Second Function which is y = -4x here the slope is negative because the slope-intercept form of the equation is .

`y=mx+b`

and the second function is

`y=-4x`

if we compare both these equations we get the value of m = -4 where m is also called the slope. So the slope of the second function is negative.

So

Option B is incorrect because the slope of the first function is positive

Option C is incorrect because the slope of the second function is negative

Option D is incorrect because the slope of the first function is 2 and the slope of the second function is -4

That leaves us with Option A which is correct, where we can see that the slope of the first function is positive and the slope of the second function is negative

Answer 2

A) The slope of function one is positive and the slope of function two is negative.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

• m - slope
• b - y-intercept

Explanation:

We see that the 1st graph has a positive slope; as x increases, the y-value also increases. Therefore, the 1st graph must have a positive slope.

We are given the equation y = -4x as our second line. Using our y = mx + b form, we see that our slope m = -4. Therefore, the 2nd graph has a negative slope.

Our answer choice then would be A, as it is the only one that matches the descriptions.