Question

1. look at the three linear functions below. show all relevant work.

graph for line a
select values from line b
equation for line c

a. which statement about the slopes is true?
a. line as slope > line bs slope > line cs slope
b. line as slope > line cs slope > line bs slope
c. line cs slope > line as slope > line bs slope
d. line bs slope > line as slope > line cs slope

b. which statement about the y - intercepts is true?
a. y - int of line a > y - int of line b > y - int line c
b. y - int of line a > y - int of line c > y - int line b
c. y - int of line c > y - int of line a > y - int line b
d. y - int of line b > y - int of line a > y - int line c

Explanation:

Step1: Find slope of Line A

From the graph, if we take two points on Line A, say (-4,0) and (0,6). Using the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_A=\frac{6 - 0}{0-(-4)}=\frac{6}{4}=\frac{3}{2}$.

Step2: Find slope of Line B

Using the two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with two points from the table of Line B, say (-7,4) and (-4,7). Then $m_B=\frac{7 - 4}{-4-(-7)}=\frac{3}{3}=1$.

Step3: Find slope of Line C

The equation of Line C is $y=\frac{7}{4}(x + 4)-2=\frac{7}{4}x+7 - 2=\frac{7}{4}x + 5$, so $m_C=\frac{7}{4}$.

Step4: Compare slopes

We have $m_C=\frac{7}{4}=1.75$, $m_A=\frac{3}{2}=1.5$, and $m_B = 1$. So $\frac{7}{4}>\frac{3}{2}>1$, which means $m_C>m_A>m_B$.

Step5: Find y - intercept of Line A

From the graph, when $x = 0$, $y=6$, so the y - intercept of Line A, $b_A = 6$.

Step6: Find y - intercept of Line B

From the table, when $x = 0$, $y = 11$, so the y - intercept of Line B, $b_B=11$.

Step7: Find y - intercept of Line C

The equation of Line C is $y=\frac{7}{4}x + 5$, so the y - intercept of Line C, $b_C = 5$.

Step8: Compare y - intercepts

We have $b_B = 11$, $b_A=6$, $b_C = 5$. So $b_B>b_A>b_C$.

Answer:

a. c. Line C's slope > Line A's slope > Line B's slope
b. d. y - int of Line B > y - int of Line A > y - int Line C