Question

topic 1: writing linear equations (given a graph)

1. write a linear equation given the graph.
2. write a linear equation given the graph.
3. identify the equation of the line graphed below. prove by converting! ( y = mx + b ) to ( ax + by = c )

a. ( 2x + y = 4 )
b. ( 2x - y = 4 )
c. ( x + 2y = 8 )
d. ( x - 2y = 8 )

1. identify the equation of the line graphed below. prove by converting!

a. ( 3x + 5y = 5 )
b. ( 3x - 5y = 5 )
c. ( 5x + 3y = 3 )
d. ( 5x - 3y = 3 )
topic 5: vertical & horizontal lines

1. ( y = -2 )
2. ( x = 5 )

Explanation:

Step1: Find slope using two points

Points: $(0,3), (-3,-3)$. Slope $m=\frac{-3-3}{-3-0}=\frac{-6}{-3}=2$

Step2: Identify y-intercept $b$

Line crosses y-axis at $(0,3)$, so $b=3$

Step3: Write slope-intercept equation

$y=2x+3$

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Step1: Find slope using two points

Points: $(0,4), (4,0)$. Slope $m=\frac{0-4}{4-0}=\frac{-4}{4}=-1$

Step2: Identify y-intercept $b$

Line crosses y-axis at $(0,4)$, so $b=4$

Step3: Write slope-intercept equation

$y=-x+4$

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Step1: Find slope and y-intercept

Points: $(0,4), (8,0)$. Slope $m=\frac{0-4}{8-0}=-\frac{1}{2}$, $b=4$. Equation: $y=-\frac{1}{2}x+4$

Step2: Convert to standard form

Multiply by 2: $2y=-x+8$, rearrange to $x+2y=8$

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Step1: Find slope and y-intercept

Points: $(0,-1), (3,4)$. Slope $m=\frac{4-(-1)}{3-0}=\frac{5}{3}$, $b=-1$. Equation: $y=\frac{5}{3}x-1$

Step2: Convert to standard form

Multiply by 3: $3y=5x-3$, rearrange to $5x-3y=3$

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Step1: Graph horizontal line $y=-2$

Draw a horizontal line passing through $y=-2$ (parallel to x-axis, intersects y-axis at $(0,-2)$)

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Step1: Graph vertical line $x=5$

Draw a vertical line passing through $x=5$ (parallel to y-axis, intersects x-axis at $(5,0)$)

Answer:

1. $y=2x+3$
2. $y=-x+4$
3. C. $x + 2y = 8$
4. D. $5x - 3y = 3$
5. (Horizontal line through $y=-2$)
6. (Vertical line through $x=5$)