Question

7.2.1 proportiona identify and use the k from tables, graphs, equa directions: finish filling in the chart below. kx format. table graph x y 0 0 1 12 2 24 3 36 x y 0 0 1 5 2 10 3 15 x y 0 0 1 8 2 16 3 24 x y 0 0 2 -10 4 -20 6 -30

Explanation:

Step1: Find first table's k value

$k = \frac{y}{x} = \frac{12}{1} = 12$

Step2: Verify first table proportionality

$\frac{24}{2}=12$, $\frac{36}{3}=12$, so $y=12x$

Step3: Find second table's k value

$k = \frac{y}{x} = \frac{5}{1} = 5$

Step4: Verify second table proportionality

$\frac{10}{2}=5$, $\frac{15}{3}=5$, so $y=5x$

Step5: Find third table's k value

$k = \frac{y}{x} = \frac{8}{1} = 8$

Step6: Verify third table proportionality

$\frac{16}{2}=8$, $\frac{24}{3}=8$, so $y=8x$

Step7: Find fourth table's k value

$k = \frac{y}{x} = \frac{-10}{2} = -5$

Step8: Verify fourth table proportionality

$\frac{-20}{4}=-5$, $\frac{-30}{6}=-5$, so $y=-5x$

Step9: List graph points for each set

1. First graph: $(0,0), (1,12), (2,24), (3,36)$
2. Second graph: $(0,0), (1,5), (2,10), (3,15)$
3. Third graph: $(0,0), (1,8), (2,16), (3,24)$
4. Fourth graph: $(0,0), (2,-10), (4,-20), (6,-30)$

Answer:

1. First table (complete, rule: $y=12x$), graph points: $(0,0), (1,12), (2,24), (3,36)$
2. Second table (complete, rule: $y=5x$), graph points: $(0,0), (1,5), (2,10), (3,15)$
3. Third table (complete, rule: $y=8x$), graph points: $(0,0), (1,8), (2,16), (3,24)$
4. Fourth table (complete, rule: $y=-5x$), graph points: $(0,0), (2,-10), (4,-20), (6,-30)$

To plot the graphs: For each set, plot the listed coordinate points and draw a straight line through them passing through the origin.