Question

$y=mx+b$

1. $y=-\frac{2}{3}x-1$
2. $y=-x-1$
3. $y=-2x-4$
4. $y=-\frac{1}{2}x-1$
5. $x=1$
6. $y=2$

directions: write th

Explanation:

All lines use the slope-intercept form $y=mx+b$ (or special cases for vertical/horizontal lines), where $m$ = slope, $b$ = y-intercept (point $(0,b)$). We find key points to plot each line.

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4) $y=-\frac{2}{3}x-1$

Step1: Identify intercepts

Y-intercept: $(0, -1)$
Set $y=0$: $0=-\frac{2}{3}x-1 \implies x=-\frac{3}{2}=-1.5$, so x-intercept $(-1.5, 0)$

Step2: Plot & draw line

Mark $(0,-1)$ and $(-1.5,0)$, connect with a straight line.

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5) $y=-x-1$

Step1: Identify intercepts

Y-intercept: $(0, -1)$
Set $y=0$: $0=-x-1 \implies x=-1$, so x-intercept $(-1, 0)$

Step2: Plot & draw line

Mark $(0,-1)$ and $(-1,0)$, connect with a straight line.

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6) $y=-2x-4$

Step1: Identify intercepts

Y-intercept: $(0, -4)$
Set $y=0$: $0=-2x-4 \implies x=-2$, so x-intercept $(-2, 0)$

Step2: Plot & draw line

Mark $(0,-4)$ and $(-2,0)$, connect with a straight line.

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7) $y=-\frac{1}{2}x-1$

Step1: Identify intercepts

Y-intercept: $(0, -1)$
Set $y=0$: $0=-\frac{1}{2}x-1 \implies x=-2$, so x-intercept $(-2, 0)$

Step2: Plot & draw line

Mark $(0,-1)$ and $(-2,0)$, connect with a straight line.

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8) $x=1$

Step1: Identify line type

Vertical line, passes through all points where $x=1$ (e.g., $(1,0), (1,2), (1,-3)$)

Step2: Plot & draw line

Mark points with $x=1$, draw vertical line.

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9) $y=2$

Step1: Identify line type

Horizontal line, passes through all points where $y=2$ (e.g., $(0,2), (3,2), (-2,2)$)

Step2: Plot & draw line

Mark points with $y=2$, draw horizontal line.

Answer:

1. For $y=-\frac{2}{3}x-1$: Line through $(0,-1)$ and $(-1.5, 0)$
2. For $y=-x-1$: Line through $(0,-1)$ and $(-1, 0)$
3. For $y=-2x-4$: Line through $(0,-4)$ and $(-2, 0)$
4. For $y=-\frac{1}{2}x-1$: Line through $(0,-1)$ and $(-2, 0)$
5. For $x=1$: Vertical line through $x=1$ (all $y$-values)
6. For $y=2$: Horizontal line through $y=2$ (all $x$-values)