Question

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

Explanation:

Problem 9: $y=3$

Step1: Identify line type

This is a horizontal line (constant $y$-value).

Step2: Locate key point

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

Step3: Plot the line

Draw a horizontal line through these points.

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Problem 10: $y=3x-2$

Step1: Identify slope-intercept form

Use $y=mx+b$, where $m=3$, $b=-2$.

Step2: Plot y-intercept

The y-intercept is $(0, -2)$.

Step3: Use slope to find next point

Slope $\frac{3}{1}$: move 1 right, 3 up from $(0,-2)$ to get $(1, 1)$.

Step4: Draw the line

Connect $(0,-2)$ and $(1,1)$, extend both ways.

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Problem 11: $y=4x+3$

Step1: Identify slope-intercept form

Use $y=mx+b$, where $m=4$, $b=3$.

Step2: Plot y-intercept

The y-intercept is $(0, 3)$.

Step3: Use slope to find next point

Slope $\frac{4}{1}$: move 1 right, 4 up from $(0,3)$ to get $(1, 7)$; or 1 left, 4 down to get $(-1, -1)$.

Step4: Draw the line

Connect these points, extend both ways.

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Problem 12: $y=\frac{6}{5}x+5$

Step1: Identify slope-intercept form

Use $y=mx+b$, where $m=\frac{6}{5}$, $b=5$.

Step2: Plot y-intercept

The y-intercept is $(0, 5)$.

Step3: Use slope to find next point

Slope $\frac{6}{5}$: move 5 right, 6 up from $(0,5)$ to get $(5, 11)$; or 5 left, 6 down to get $(-5, -1)$.

Step4: Draw the line

Connect these points, extend both ways.

Answer:

1. For $y=3$: A horizontal line passing through all points with $y$-coordinate 3.
2. For $y=3x-2$: A line with y-intercept $(0,-2)$ and slope 3, passing through $(1,1)$.
3. For $y=4x+3$: A line with y-intercept $(0,3)$ and slope 4, passing through $(1,7)$.
4. For $y=\frac{6}{5}x+5$: A line with y-intercept $(0,5)$ and slope $\frac{6}{5}$, passing through $(5,11)$.