Question

(a) Which function has the graph with the greatest y-intercept? Function 1Function 2 Function 3 Function 4(b) Which function has the graph with a y-intercept closest to 0?(c) Which functions have graphs with slopes less than 4? (Check all that apply.) Function 1Function 2 Function 3Function 4

Answer 1

ANSWER:

EXPLANATION:

Given:

Let's go ahead and determine the y-intercept and slope of each of the functions;

For Function 1:

The y-intercept of a graph is the point on the graph where the line crosses the y-axis.

Looking at the graph of Function 1, we can see that the line crosses the y-axis at y = -4, so the y-intercept is -4

We'll now use the points (0, -4) and (1, -2) to determine the slope(m) of the line using the below slope formula;

$\begin{gathered} Slope(m)=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-2-(-4)}{1-0} \\ =\frac{-2+4}{1} \\ =2 \end{gathered}$

So the slope(m) of Function 1 is 2

For Function 2:

Note the y-intercept is the value of y when x = 0.

So from the given table, we can see that the y-intercept is 5

We'll now use the points (0, 5) and (2, 3) to determine the slope(m) of the function using the below slope formula;

$\begin{gathered} Slope(m)=\frac{3-5}{2-0} \\ =-\frac{2}{2} \\ =-1 \end{gathered}$

So the slope of Function 2 is -1

For Function 3:

Recall that the slope-intercept form of the equation of a line is generally given as;

$y=mx+b$

where;

m = slope of the line

b = y-intercept of the line

Given the function;

$y=-3x-2$

We can see that the slope(m) of the function -3 and the y-intercept(b) is -2

For Function 4:

The slope-intercept is 5 and the y-intercept is 1

a) From the above, we can see that the function with the greatest y-intercept is Function 2

b) From the above, we can see that the function with the y-intercept closest to 0 is Function 2

c) The functions that have graphs with slopes less than 4 are Function 1, Function 2, and Function 3