Let’s solve each equation step by step. We’ll graph them using slope-intercept form:
y = mx + b, where:
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m is the slope (rise over run)
-
b is the y-intercept (where the line crosses the y-axis)
We’ll go one by one.
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1. y = 2x + 4
- y-intercept: (0, 4) → start here
- slope: 2/1 → go up 2, right 1 from (0,4) to get (1,6), then (2,8), etc.
- Also go down 2, left 1 to get (-1,2), (-2,0), etc.
Plot those points and draw a straight line.
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2. y = -½x + 2
- y-intercept: (0, 2)
- slope: -½ → go down 1, right 2 → (2,1), (4,0)
- Or up 1, left 2 → (-2,3), (-4,4)
Draw line through these.
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3. y = ¾x + ¼
- y-intercept: (0, 0.25) — that’s just above 0 on y-axis
- slope: ¾ → up 3, right 4 → from (0,0.25) to (4, 3.25)
- Or down 3, left 4 → (-4, -2.75)
You can also pick easy x-values to plot:
If x=0 → y=0.25
If x=4 → y=¾(4)+¼ = 3 + 0.25 = 3.25
If x=-4 → y=¾(-4)+¼ = -3 + 0.25 = -2.75
Plot those and connect.
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4. y = x – 5
- y-intercept: (0, -5)
- slope: 1/1 → up 1, right 1 → (1,-4), (2,-3), etc.
- Down 1, left 1 → (-1,-6), (-2,-7)
Easy to plot.
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5. y = -7x + 2
- y-intercept: (0, 2)
- slope: -7/1 → very steep! Down 7, right 1 → (1, -5)
- Up 7, left 1 → (-1, 9)
This line drops fast. Plot (0,2) and (1,-5), draw line.
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6. y = ⅔x
- This is same as y = ⅔x + 0 → y-intercept at (0,0)
- slope: ⅔ → up 2, right 3 → (3,2), (6,4)
- Down 2, left 3 → (-3,-2), (-6,-4)
Start at origin, use slope to find more points.
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7. y = -¼x + 4
- y-intercept: (0,4)
- slope: -¼ → down 1, right 4 → (4,3), (8,2)
- Up 1, left 4 → (-4,5), (-8,6)
Gentle downward slope.
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8. y = 5
- Horizontal line! Always y=5, no matter what x is.
- So plot points like (0,5), (1,5), (-3,5), etc.
- Draw flat line across at y=5.
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9. y = ½x – 3
- y-intercept: (0, -3)
- slope: ½ → up 1, right 2 → (2,-2), (4,-1)
- Down 1, left 2 → (-2,-4), (-4,-5)
Plot and connect.
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✔ All equations are now ready to be graphed. For each, you:
1. Start at the y-intercept (the “+ b” part).
2. Use the slope (“m”) to find another point.
3. Draw a straight line through them.
Remember: if slope is negative, the line goes downhill from left to right. If positive, it goes uphill.
Final Answer: Graph each equation using its y-intercept and slope as explained above. Each line should pass through the calculated points based on the slope and intercept.
Parent Tip: Review the logic above to help your child master the concept of linear equation graphs worksheet.
