Worksheet with eight graphs of lines on coordinate planes, each requiring the student to write the equation in slope-intercept form.

To solve this worksheet, we need to write the slope-intercept form of each line shown in the graphs. The slope-intercept form is:

> y = mx + b

Where:
- m is the slope of the line (rise over run),
- b is the y-intercept (where the line crosses the y-axis).

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Let’s go through each graph one by one.

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1) Graph 1

- Line passes through: (0, -1) and (-3, 2) (or you can pick any two clear points).
- Slope (m) = (change in y)/(change in x) = (2 - (-1)) / (-3 - 0) = 3 / (-3) = -1
- Y-intercept (b) = -1 (crosses y-axis at (0, -1))
✔ Equation: y = -x - 1

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2) Graph 2

- Line passes through: (0, 1) and (4, -1).
- Slope (m) = (-1 - 1)/(4 - 0) = (-2)/4 = -1/2
- Y-intercept (b) = 1
✔ Equation: y = -½x + 1

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3) Graph 3

- Line passes through: (0, 2) and (-2, -2).
- Slope (m) = (-2 - 2)/(-2 - 0) = (-4)/(-2) = 2
- Y-intercept (b) = 2
✔ Equation: y = 2x + 2

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4) Graph 4

- This is a vertical line at x = -2.
- Vertical lines do not have a slope-intercept form because slope is undefined.
- But if forced to write an equation, it's x = -2 — however, this is not in slope-intercept form.
⚠️ Note: Since the problem asks for “slope-intercept form”, and vertical lines cannot be written in that form, this might be a trick question or error. But technically, no slope-intercept equation exists for vertical lines.

✔ Answer: Not possible (undefined slope)
*(If required to write something, say “x = -2” but note it’s not slope-intercept)*

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5) Graph 5

- Line passes through: (0, -2) and (2, 2).
- Slope (m) = (2 - (-2))/(2 - 0) = 4/2 = 2
- Y-intercept (b) = -2
✔ Equation: y = 2x - 2

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6) Graph 6

- Line passes through: (0, -1) and (4, 0).
- Slope (m) = (0 - (-1))/(4 - 0) = 1/4
- Y-intercept (b) = -1
✔ Equation: y = ¼x - 1

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7) Graph 7

- Line passes through: (0, 1) and (4, 0).
- Slope (m) = (0 - 1)/(4 - 0) = -1/4
- Y-intercept (b) = 1
✔ Equation: y = -¼x + 1

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8) Graph 8

- Line passes through: (0, 2) and (-2, -2).
- Slope (m) = (-2 - 2)/(-2 - 0) = (-4)/(-2) = 2
- Y-intercept (b) = 2
✔ Equation: y = 2x + 2

*(Same as Graph 3 — possibly intentional or duplicate)*

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## ✔ Final Answers:

1) y = -x - 1
2) y = -½x + 1
3) y = 2x + 2
4) Not possible (vertical line) — or x = -2 (but not slope-intercept)
5) y = 2x - 2
6) y = ¼x - 1
7) y = -¼x + 1
8) y = 2x + 2

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📌 Tip for Students: Always find two clear points on the line, calculate slope (rise/run), then identify where the line crosses the y-axis (b). Plug into y = mx + b.

Let me know if you want step-by-step visuals or practice problems!