Question

The table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x f(x) 0 1 2 4 4 7 g(x) = 2x + 1

Answer 1

Answer:

y-intercept of f(x) = 1

y-intercept of g(x) = 1

The slope of f(x) = 1.5

The slope of g(x) = 2

Step-by-step explanation:

 x   :   0    2    4

f(x) :   1     4    7

The table x , f(x) represents a linear function

The linear function has the form y = mx + c

where m is the slope and c is y-intercept

m = (y₂-y₁)/(x₂-x₁) = (7-4)/(4-2) = 3/2 = 1.5

y-intercept is the value of y at which x = 0

From the table at x = 0 ⇒y= f(x) = 1 ⇒ c = 1

∴ f(x) = 1.5x + 1

And given g(x) = 2x + 1

We will Compare the y-intercepts and slopes of the linear functions f(x) and g(x)

y-intercept of f(x) = 1

y-intercept of g(x) = 1

The slope of f(x) = 1.5

The slope of g(x) = 2

So, y-intercept of f(x) = y-intercept of g(x) = 1

And The slope of g(x) is greater than The slope of f(x)