Question

name: prealgebra hw q3 - 1 due: friday, january 9, 2026 1 write the equation of the lines below in slope - intercept form. (three graphs of lines on coordinate planes with spaces for slope (m), y - intercept (b), and equation) 2 graph the line below: $y = -\frac{1}{3}x + 5$ (a coordinate grid is provided) 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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[1] First Graph (Left)

Step1: Identify slope ($m$)

Slope is rise over run: $\frac{3}{1}=3$

Step2: Identify y-intercept ($b$)

Line crosses y-axis at $y=-4$

Step3: Write slope-intercept form

Slope-intercept: $y=mx+b$
$y=3x-4$

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[1] Second Graph (Middle)

Step1: Identify slope ($m$)

Slope is rise over run (negative): $\frac{-3}{2}$

Step2: Identify y-intercept ($b$)

Line crosses y-axis at $y=4$

Step3: Write slope-intercept form

Slope-intercept: $y=mx+b$
$y=-\frac{3}{2}x+4$

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[1] Third Graph (Right)

Step1: Identify slope ($m$)

Slope is rise over run: $\frac{5}{4}$

Step2: Identify y-intercept ($b$)

Line crosses y-axis at $y=4$

Step3: Write slope-intercept form

Slope-intercept: $y=mx+b$
$y=\frac{5}{4}x+4$

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[2] Graph $y=-\frac{1}{3}x+5$

Step1: Mark y-intercept ($b$)

Plot point $(0, 5)$

Step2: Use slope to find second point

Slope $-\frac{1}{3}$: right 3, down 1 → $(3, 4)$

Step3: Draw line through points

Connect $(0,5)$ and $(3,4)$, extend both ends

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[3a] Yoga Studio Equation

Step1: Define variables

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

Step2: Identify slope ($m$)

Per-class fee: $m=5$

Step3: Identify y-intercept ($b$)

Annual fee: $b=100$

Step4: Write slope-intercept form

$y=5x+100$

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[3b] Cost for 15 classes

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 graph: $y=3x-4$

Middle graph: $y=-\frac{3}{2}x+4$
Right graph: $y=\frac{5}{4}x+4$

1. (Graph with points $(0,5)$ and $(3,4)$, line connecting them)

3a. $y=5x+100$
3b. $\$175$