Question

I need the answer and the work it asks for

Answer 1

Part A. Write a sentence to compare the slope of the two functions given and show the steps in determining the slopes.

Note: In order to compare the slopes, we first needed to get the slopes of each given.

First, let's deal with the f(x) table.

x -1 0 1

f(x) -3 0 3

Note: f(x) can be also y.

In order to find the slope, we are going to use this formula: (Slope of a line formula)

`\begin{gathered} m\text{ = }\frac{rise\text{ }}{run}\text{= }\frac{y_{2_{}}_{}-y_1}{x_2-x_1_{}} \\ \text{Let us assign values from the table above.} \\ y_{2_{}}\text{ = -3 , }y_1\text{ = 0} \\ x_2=-1,x_1=0 \\ \text{Then, we should substitute it in the formula.} \\ m\text{ = }\frac{y_{2_{}}-y_1}{x_2-x_1}\text{ =}(-3-0)/(-1-0)\text{ = }(-3)/(-1)\text{ = 3} \\ \text{Note: m is also the slope.} \end{gathered}`

Note: When finding y-intercept from a table, you find the y-value when the x-value is equal to zero.

y-intercept = 0 because it is the value from the table where x is equal to zero.

Second, g(x) = 7x +2

In this case, we should use the slope-intercept form.

`\begin{gathered} \text{Slope - Intercept Form} \\ y=\text{ mx + b} \\ \text{where m = slope and b = y - intercept} \\ m\text{ = 7} \\ y\text{ - intercept = 2} \end{gathered}`

Comparison: The slope of g(x) which is 7 is greater than the slope of f(x) which is 3.

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

Answer: G(x) has a greater y-intercept compared to that of f(x). The y-intercept of g(x) is equal to 2 while the y-intercept of f(x) is equal to 0.

Note: In the question "justify your answer", you can refer to the explanation above where we solved for the y-intercept.