Question

spiral review
date:
period:
problems 9–10: solve each equation. show your thinking.

1. $-4(r + 2) = 4(2 - 2r)$
2. $1.3 + 6d = 2.7 - 8d$
3. these two lines are parallel. write an equation for each line.

line a:
line b:
(graph of two parallel lines a and b on a coordinate plane, with line a passing through (5, 4) and the origin, line b passing through (0, -3.2) and (4, 0))

Explanation:

Problem 9

Step1: Expand both sides

$-4r - 8 = 8 - 8r$

Step2: Add $8r$ to both sides

$-4r + 8r - 8 = 8$
$4r - 8 = 8$

Step3: Add 8 to both sides

$4r = 8 + 8$
$4r = 16$

Step4: Divide by 4

$r = \frac{16}{4}$

Problem 10

Step1: Add $8d$ to both sides

$1.3 + 6d + 8d = 2.7$
$1.3 + 14d = 2.7$

Step2: Subtract 1.3 from both sides

$14d = 2.7 - 1.3$
$14d = 1.4$

Step3: Divide by 14

$d = \frac{1.4}{14}$

Problem 11

Step1: Find slope of Line a

Use points $(0,0)$ and $(5,4)$:
$m = \frac{4-0}{5-0} = \frac{4}{5} = 0.8$

Step2: Equation for Line a

Y-intercept is $0$, so $y = 0.8x$

Step3: Equation for Line b

Parallel lines have same slope. Use point $(0,-3.2)$:
$y = 0.8x - 3.2$

Answer:

Problem 9: $r = 4$
Problem 10: $d = 0.1$
Problem 11:
Line a: $y = 0.8x$
Line b: $y = 0.8x - 3.2$