Questions: 1. y=-3x 2. x+y-5=0 3. 3x+y=5 4. y=(-x+7)/3 5. y=2 6. x+4y-4=0 7. Which two lines in Exercises 1-6 are parallel? Explain.

Transcript text: 1. $y=-3 x$ 2. $x+y-5=0$ 3. $3 x+y=5$ 4. $y=\frac{-x+7}{3}$ 5. $y=2$ 6. $x+4 y-4=0$ 7. Which two lines in Exercises 1-6 are parallel? Explain.

Solution

Solution Steps

Step 1: Rewrite the equation in slope-intercept form for Exercise 1

The given equation is $ y = -3x $. This is already in slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

Slope $ m = -3 $
Y-intercept $ b = 0 $

Step 2: Rewrite the equation in slope-intercept form for Exercise 2

The given equation is $ x + y - 5 = 0 $. Solve for $ y $:

\[ x + y - 5 = 0 \\ y = -x + 5 \]

Now, the equation is in slope-intercept form $ y = mx + b $.

Slope $ m = -1 $
Y-intercept $ b = 5 $

Step 3: Rewrite the equation in slope-intercept form for Exercise 3

The given equation is $ 3x + y = 5 $. Solve for $ y $:

\[ 3x + y = 5 \\ y = -3x + 5 \]

Now, the equation is in slope-intercept form $ y = mx + b $.

Slope $ m = -3 $
Y-intercept $ b = 5 $

Final Answer

$ m = -3, b = 0 $
$ m = -1, b = 5 $
$ m = -3, b = 5 $

The two lines that are parallel are from Exercises 1 and 3, as they both have the same slope $ m = -3 $.

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