Question

how do kangaroos travel across the ocean?
write the letter of each answer in the box containing the exercise number.
write the linear equation in slope - intercept form.

1. $3x + y = 8$
2. $9x - y=\frac{1}{3}$
3. $-\frac{1}{4}x + y = 3$
4. $2x - 7y = 12$

find the $x$- and $y$-intercepts of the linear equation.

1. $-3x + 5y = 15$
2. $2x - y = 4$
3. $4x - 9y = 36$
4. $x+\frac{1}{3}y=-3$
5. $\frac{2}{5}x-\frac{3}{4}y = 12$
6. $7.6x + 15.2y = 38$
7. the booster club sells popcorn at basketball games for $0.75 per bag. their cost for supplies is $12. the equation $-0.75x + y=-12$ represents the booster clubs income $y$ after selling $x$ bags of popcorn. find the $x$- and $y$-intercepts of the linear equation.
8. you upload digital photos to an online photo processing website. you can print 4 - inch - by - 6 - inch photos for $0.30 each and 5 - inch - by - 7 - inch photos for $0.75 each. the linear equation $0.30x + 0.75y = 15$ represents the ways you can print $x$ 4 - inch - by - 6 - inch photos and $y$ 5 - inch - by - 7 - inch photos for $15. find the $x$- and $y$-intercepts of the linear equation.

answers
h. $y=\frac{2}{7}x-\frac{12}{7}$
s. $x$-intercept: 5; $y$-intercept: 2.5
h. $x$-intercept: - 3; $y$-intercept: - 9
j. $x$-intercept: 50; $y$-intercept: 20
m. $x$-intercept: 2; $y$-intercept: - 4
y. $x$-intercept: 30; $y$-intercept: - 16
u. $x$-intercept: 9; $y$-intercept: - 4
p. $x$-intercept: 16; $y$-intercept: - 12
t. $y=-3x + 8$
e. $x$-intercept: - 5; $y$-intercept: 3
p. $y = 9x-\frac{1}{3}$
i. $y=\frac{1}{4}x + 3$

Explanation:

Step1: Rewrite to slope-intercept form ($y=mx+b$)

$3x + y = 8 \implies y = -3x + 8$

Step2: Rewrite to slope-intercept form ($y=mx+b$)

$9x - y = \frac{1}{3} \implies y = 9x - \frac{1}{3}$

Step3: Rewrite to slope-intercept form ($y=mx+b$)

$-\frac{1}{4}x + y = 3 \implies y = \frac{1}{4}x + 3$

Step4: Rewrite to slope-intercept form ($y=mx+b$)

$2x - 7y = 12 \implies -7y = -2x + 12 \implies y = \frac{2}{7}x - \frac{12}{7}$

Step5: Find x/y-intercepts (set y/x=0)

x-intercept: $-3x = 15 \implies x = -5$; y-intercept: $5y = 15 \implies y = 3$

Step6: Find x/y-intercepts (set y/x=0)

x-intercept: $2x = 4 \implies x = 2$; y-intercept: $-y = 4 \implies y = -4$

Step7: Find x/y-intercepts (set y/x=0)

x-intercept: $4x = 36 \implies x = 9$; y-intercept: $-9y = 36 \implies y = -4$

Step8: Find x/y-intercepts (set y/x=0)

x-intercept: $x = -3$; y-intercept: $\frac{1}{3}y = -3 \implies y = -9$

Step9: Find x/y-intercepts (set y/x=0)

x-intercept: $\frac{2}{5}x = 12 \implies x = 30$; y-intercept: $-\frac{3}{4}y = 12 \implies y = -16$

Step10: Find x/y-intercepts (set y/x=0)

x-intercept: $7.6x = 38 \implies x = 5$; y-intercept: $15.2y = 38 \implies y = 2.5$

Step11: Find x/y-intercepts (set y/x=0)

x-intercept: $-0.75x = -12 \implies x = 16$; y-intercept: $y = -12$

Step12: Find x/y-intercepts (set y/x=0)

x-intercept: $0.30x = 15 \implies x = 50$; y-intercept: $0.75y = 15 \implies y = 20$

Answer:

1. T
2. P
3. I
4. H
5. E
6. M
7. U
8. H
9. Y
10. S
11. P
12. J

(Boxed letter order for the puzzle: T, H, E, Y, J, U, M, S, I, P, H, T → "THEY JUMP SHIP")