Question

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

Explanation:

Step1: Identify slope-intercept form

The slope-intercept form of a line is $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

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For equation 3) $y=x+1$

Step2: Identify $m$ and $b$

Here $m=1$, $b=1$.

Step3: Plot y-intercept

Mark the point $(0,1)$ on the grid.

Step4: Use slope to find next point

Slope $1=\frac{1}{1}$: move 1 up, 1 right from $(0,1)$ to $(1,2)$. Draw a line through these points.

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For equation 4) $y=\frac{4}{3}x-4$

Step2: Identify $m$ and $b$

Here $m=\frac{4}{3}$, $b=-4$.

Step3: Plot y-intercept

Mark the point $(0,-4)$ on the grid.

Step4: Use slope to find next point

Slope $\frac{4}{3}$: move 4 up, 3 right from $(0,-4)$ to $(3,0)$. Draw a line through these points.

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For equation 5) $y=-3x-3$

Step2: Identify $m$ and $b$

Here $m=-3$, $b=-3$.

Step3: Plot y-intercept

Mark the point $(0,-3)$ on the grid.

Step4: Use slope to find next point

Slope $-3=\frac{-3}{1}$: move 3 down, 1 right from $(0,-3)$ to $(1,-6)$. Draw a line through these points.

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For equation 6) $y=4$ (skipped per instruction)

This is a horizontal line through $(0,4)$, parallel to the x-axis.

Answer:

1. For $y=x+1$: Line through $(0,1)$ and $(1,2)$ with slope 1.
2. For $y=\frac{4}{3}x-4$: Line through $(0,-4)$ and $(3,0)$ with slope $\frac{4}{3}$.
3. For $y=-3x-3$: Line through $(0,-3)$ and $(1,-6)$ with slope $-3$.
4. $y=4$ is skipped as instructed.