Worksheet for graphing linear functions with equations and coordinate grids.

Let’s solve each problem step by step. We’re graphing linear equations in the form y = mx + b, where:

- m is the slope (rise over run)
- b is the y-intercept (where the line crosses the y-axis)

We’ll find two points for each equation, plot them, and draw a straight line through them.

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Problem 1: y = -3x + 2

Step 1: Find the y-intercept → when x = 0, y = 2 → point (0, 2)

Step 2: Use slope = -3/1 → from (0,2), go down 3, right 1 → (1, -1)

Check another point: if x = 2, y = -3(2)+2 = -6+2 = -4 → (2, -4)

Plot (0,2), (1,-1), (2,-4) and draw line.

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Problem 2: y = -2x - 4

Step 1: y-intercept → x=0 → y=-4 → (0, -4)

Step 2: slope = -2/1 → from (0,-4), go down 2, right 1 → (1, -6)

Check: x=2 → y=-2(2)-4 = -8 → (2, -8)

Plot (0,-4), (1,-6), (2,-8) and draw line.

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Problem 3: y = 2x - 4

Step 1: y-intercept → x=0 → y=-4 → (0, -4)

Step 2: slope = 2/1 → up 2, right 1 → (1, -2)

Check: x=2 → y=2(2)-4 = 0 → (2, 0)

Plot (0,-4), (1,-2), (2,0) and draw line.

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Problem 4: y = (1/2)x - 4

Step 1: y-intercept → x=0 → y=-4 → (0, -4)

Step 2: slope = 1/2 → up 1, right 2 → (2, -3)

Check: x=4 → y=(1/2)(4)-4 = 2-4 = -2 → (4, -2)

Plot (0,-4), (2,-3), (4,-2) and draw line.

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Problem 5: y = (2/3)x - 5

Step 1: y-intercept → x=0 → y=-5 → (0, -5)

Step 2: slope = 2/3 → up 2, right 3 → (3, -3)

Check: x=6 → y=(2/3)(6)-5 = 4-5 = -1 → (6, -1)

Plot (0,-5), (3,-3), (6,-1) and draw line.

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Problem 6: y = (6/5)x + 9

Step 1: y-intercept → x=0 → y=9 → (0, 9)

Step 2: slope = 6/5 → up 6, right 5 → (5, 15) — but 15 is off the grid! Let’s pick smaller steps.

Try x = 5 → y = (6/5)(5) + 9 = 6 + 9 = 15 → too high.

Try x = -5 → y = (6/5)(-5) + 9 = -6 + 9 = 3 → (-5, 3)

That’s on the grid!

Another point: x = 0 → (0,9)

x = 5 → too high, so use x = -5 and x = 0.

Or try x = 5/6? Not nice. Better to use integer x values that give integer y.

Wait — let’s try x = 5 → y=15 (off chart). Try x = -5 → y=3 (good).

Try x = 0 → y=9 (good).

Try x = 5 → too big. What about x = -10?

y = (6/5)(-10) + 9 = -12 + 9 = -3 → (-10, -3)

Perfect! So we have:

(-10, -3), (0, 9), and maybe (5,15) but skip it since off grid.

Use (-10, -3) and (0,9) to draw the line.

Slope check: from (-10,-3) to (0,9): rise = 12, run = 10 → 12/10 = 6/5 ✔️

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Now, here are the final answers — which are the graphs you would draw based on these points.

Since we can’t draw here, I’ll list key points for each graph so you can plot them accurately.

Final Answer:

1. Points: (0,2), (1,-1), (2,-4)
2. Points: (0,-4), (1,-6), (2,-8)
3. Points: (0,-4), (1,-2), (2,0)
4. Points: (0,-4), (2,-3), (4,-2)
5. Points: (0,-5), (3,-3), (6,-1)
6. Points: (-10,-3), (0,9), (5,15) — but only plot (-10,-3) and (0,9) since 15 is off grid; or use (-5,3) as middle point.

For #6, better usable points within grid: (-10, -3), (-5, 3), (0, 9)

✔ All lines should be straight and pass through these points.