Question

The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −15
0 −10
1 −5

g(x)

g(x) = 2x + 8

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).

Part B: Which function has a greater y-intercept? Justify your answer.

Answer 1

Explanation:

If you want to compare the 2 slopes, you first have to know what they are. From the table we can find it by plugging in some numbers to the slope formula and doing the math on it:

`m=(-10-(-15))/(0-(-1))`

which gives us a slope of 5.

From the equation, which is in y = mx + b form, m stands for slope. The number in the m position is 2. In a sentence:

The slope found in the values from the table, 5, is greater than the slope found in the linear equation, 2.

Part B: The y-intercept exists where x = 0. Looking at the values in the table, where x = 0, y = -10. So the y-intercept of the line in the table is -10. In y = mx + b, the linear equation, 8 = b, which is also the y-intercept. So the y-intercept in the table is -10 and the y-intercept in the equation is 8. The y-intercept is greater in the equation than in the table because 8 is greater than -10