Question

name:
puealgebra 1tw q3 # 1

1 write the equation of the line below in slope - intercept form.

m =
b =
equation:

m =
b =
equation:

m =
b =
equation:

2 graph the line below:
$y = -\frac{1}{2}x + 6$

3 in order to join a yoga studio there is a $100 annual fee and a $5 fee for each class you attend.
a. write an equation in slope - intercept form that models this situation.

b. if you attend 15 classes, how much would it cost you?

Explanation:

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Part 1: Write line equations (slope-intercept: $y=mx+b$, where $m$=slope, $b$=y-intercept)

Line 1 (Left)

Step1: Calculate slope ($m$)

Slope formula: $m=\frac{\Delta y}{\Delta x}=\frac{2}{1}=2$

Step2: Identify y-intercept ($b$)

The line crosses y-axis at $b=-1$

Step3: Write equation

$y=2x-1$

Line 2 (Middle)

Step1: Calculate slope ($m$)

$m=\frac{\Delta y}{\Delta x}=\frac{-3}{2}=-1.5$

Step2: Identify y-intercept ($b$)

The line crosses y-axis at $b=3$

Step3: Write equation

$y=-\frac{3}{2}x+3$

Line 3 (Right)

Step1: Calculate slope ($m$)

$m=\frac{\Delta y}{\Delta x}=\frac{1}{3}$

Step2: Identify y-intercept ($b$)

The line crosses y-axis at $b=2$

Step3: Write equation

$y=\frac{1}{3}x+2$

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Part 2: Graph $y=-\frac{1}{2}x+5$

Step1: Identify y-intercept

Plot point $(0,5)$ (where $x=0$)

Step2: Use slope to find 2nd point

Slope $m=-\frac{1}{2}$: move 2 right, 1 down from $(0,5)$ to $(2,4)$

Step3: Draw line

Connect $(0,5)$ and $(2,4)$, extend both ends.

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Part 3: Yoga Studio Costs

Part 3a

Step1: Define variables

Let $x$ = number of classes, $y$ = total cost

Step2: Assign slope and intercept

$m=5$ (per-class fee), $b=100$ (annual fee)

Step3: Write slope-intercept equation

$y=5x+100$

Part 3b

Step1: Substitute $x=15$ into equation

$y=5(15)+100$

Step2: Calculate total cost

$y=75+100=175$

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Answer:

1. Left line:

$m=2$, $b=-1$, Equation: $y=2x-1$
Middle line:
$m=-\frac{3}{2}$, $b=3$, Equation: $y=-\frac{3}{2}x+3$
Right line:
$m=\frac{1}{3}$, $b=2$, Equation: $y=\frac{1}{3}x+2$

1. Graph: Plot $(0,5)$ and $(2,4)$, draw a straight line through them.
2. a. $y=5x+100$

b. $\$175$