Question

solve.
7 a line has the equation $4y = 3x - 8$. write an equation of a line parallel to the given line that has a $y$-intercept of 2.

8 a line has the equation $3y = 3 - 2x$. write an equation of a line parallel to the given line that has a $y$-intercept of 5.

9 mathematical habit 3 construct viable arguments
anna says that the graphs of $y = -3x + 7$ and $y = 3x - 7$ are parallel lines. do you agree?
explain.

Explanation:

Step1: 整理原直线为斜截式

将$4y=3x-8$变形为$y=kx+b$形式：
$y=\frac{3}{4}x-2$，得斜率$k=\frac{3}{4}$

Step2: 利用平行直线斜率相等

平行直线斜率相同，且y截距为2，代入斜截式：
$y=\frac{3}{4}x+2$
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Step1: 整理原直线为斜截式

将$3y=3-2x$变形为$y=kx+b$形式：
$y=-\frac{2}{3}x+1$，得斜率$k=-\frac{2}{3}$

Step2: 利用平行直线斜率相等

平行直线斜率相同，且y截距为5，代入斜截式：
$y=-\frac{2}{3}x+5$
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Step1: 明确平行直线判定规则

平行直线的斜率必须相等

Step2: 对比两条直线的斜率

直线$y=-3x+7$斜率为$-3$，直线$y=3x-7$斜率为$3$，二者不相等

Answer:

1. $y=\frac{3}{4}x+2$
2. $y=-\frac{2}{3}x+5$
3. 不同意。因为平行直线的斜率必须相等，而$y=-3x+7$的斜率为$-3$，$y=3x-7$的斜率为$3$，两个斜率不相等，所以这两条直线不是平行线。