Graphing Linear Equations Worksheet with six equations to plot on coordinate grids.

You’re given a worksheet titled “Graphing Linear Equations” with 6 linear equations to graph on coordinate planes. Since I can’t see the actual image or grid, I’ll explain how to graph each equation step by step, including how to choose points and scale the axes if needed.

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## 📌 General Strategy for Graphing Linear Equations:

1. Identify the form: Most are in slope-intercept form (y = mx + b), except #5 which is in standard form.
2. Find two or three points that satisfy the equation.
3. Plot the points on the coordinate plane.
4. Draw a straight line through them.
5. Label axes if scaling is changed (e.g., if you use every 2 units instead of 1).

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## 🔢 Let’s solve each one:

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1) y = 2x – 3

- This is in slope-intercept form: slope = 2, y-intercept = –3.
- Point 1: When x = 0 → y = 2(0) – 3 = –3 → (0, –3)
- Point 2: When x = 1 → y = 2(1) – 3 = –1 → (1, –1)
- Point 3: When x = 2 → y = 4 – 3 = 1 → (2, 1)

✔ Plot these 3 points and draw a line through them.

> *Note: The line rises steeply since slope = 2.*

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2) y = –3x + 2

- Slope = –3, y-intercept = 2.
- Point 1: x = 0 → y = 2 → (0, 2)
- Point 2: x = 1 → y = –3(1) + 2 = –1 → (1, –1)
- Point 3: x = –1 → y = –3(–1) + 2 = 5 → (–1, 5)

✔ Plot these. Line falls steeply (slope = –3).

> *If your grid only goes from –5 to 5, (–1,5) fits. If not, adjust scale or pick x=0.5: y = –3(0.5)+2 = 0.5 → (0.5, 0.5)*

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3) y = (1/2)x – 5

- Slope = 1/2, y-intercept = –5.
- Point 1: x = 0 → y = –5 → (0, –5)
- Point 2: x = 2 → y = (1/2)(2) – 5 = 1 – 5 = –4 → (2, –4)
- Point 3: x = 4 → y = 2 – 5 = –3 → (4, –3)

✔ Plot these. Line rises gently.

> *Since y-intercept is –5, make sure your y-axis goes down to at least –5. You may need to label every 1 unit or scale accordingly.*

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4) y = –(2/3)x + 4

- Slope = –2/3, y-intercept = 4.
- Point 1: x = 0 → y = 4 → (0, 4)
- Point 2: x = 3 → y = –(2/3)(3) + 4 = –2 + 4 = 2 → (3, 2)
- Point 3: x = –3 → y = –(2/3)(–3) + 4 = 2 + 4 = 6 → (–3, 6)

✔ Plot these. Line falls gently.

> *To avoid fractions, pick multiples of 3 for x-values. If grid is small, use x=0, x=3, x=6 → y=4, 2, 0.*

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5) x + y = 4

This is in standard form. Convert to slope-intercept or find intercepts.

#### Method: Find x- and y-intercepts.

- y-intercept: Set x = 0 → 0 + y = 4 → y = 4 → (0, 4)
- x-intercept: Set y = 0 → x + 0 = 4 → x = 4 → (4, 0)
- Another point: Let x = 2 → 2 + y = 4 → y = 2 → (2, 2)

✔ Plot (0,4), (4,0), (2,2) — this is a diagonal line from top-left to bottom-right.

> *Slope = –1 (since y = –x + 4).*

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6) y = 3

This is a horizontal line.

- Every point has y-coordinate = 3, regardless of x.
- Pick any x-values:
- (–2, 3)
- (0, 3)
- (2, 3)
- (4, 3)

✔ Draw a straight horizontal line through y = 3.

> *This line is parallel to the x-axis.*

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## 📏 Scaling Tip:

If your grid doesn’t have enough space (e.g., y = –5 or y = 6), you can:

- Label every 2 units instead of 1 (so each grid square = 2 units).
- Or, choose different x-values to keep y within range (e.g., for y = ½x – 5, use x=10 → y=0, x=8 → y=–1, etc.).

Just remember to label your axes clearly if you change the scale!

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## ✔ Final Checklist for Each Graph:

- ✔️ Two or three accurate points plotted
- ✔️ Straight line drawn through them
- ✔️ Axes labeled appropriately (especially if scaled)
- ✔️ Equation written near the graph (optional but good practice)

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Let me know if you want printable versions of these graphs or want me to generate coordinates for specific scales!